Showing posts with label 10-Maths. Show all posts
Showing posts with label 10-Maths. Show all posts

Thursday, February 24, 2022

Application of Trignometry - Ncert solutions Class 10 Maths

 Application of Trignometry - Ncert solutions Class 10 Maths 



Que 1

Circus artists climbing a 20 m long rope which is tightly stretched and tight from the top of a vertical pole to the ground find the height of the pole if the angle made by the rope with the ground level is 30 °

Solution--

Height of pole = 20×sin 30° = 20 ×1/2= 10 m 


Que 2

A tree breaks due to storm and the broken part bend so that the top of the tree touches the ground making an angle 30 ° with it the distance between the foot  of the tree  to the point where the top touches the ground is 8 m find the height of the tree

Solution--8√3 m


Que 3

A contractor plans to install two slides for the children to play in the park for the children below the age of 5 years she prefers to have a slide whose top is at the height of 1.5 m and is inclined at an angle of 30 °  to the ground where is for the elder children she wants to have a steep right at a height of 3 m and inclined at an angle of 
60 ° to the ground what should be the length of the slide in each case?

Solution--- 3m,2√3 m

Que 4 

The angle of elevation of the top of a tower from a point on the ground which is 30 metre away from the foot of the tower is.  30 °  find the height of the tower


Solution--- 10√3m


Que 5 

A kite is flying at a height of 60 m above the ground the string attached to the kite is temporary tied to a point on the ground the inclination of the string with the ground is 60 ° find the length of the string


Solution --40√3 m


Que 6 

1.5 m tall boy is standing at some distance from a 30 metre tall building the angle of elevation from his eyes to the top of the building increases from 30 ° to 60 °  as he walks towards the building find the distance he walked towards the building

Solution-- 19√3 m 

Que 7 

From a point on the ground the angle of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are 45 degree and 60 degree respectively find the height of the tower

Solution -- 20(√3-1) m


Que 8 

A statue 1.6 m tall stands on the top of a pedestal from a point on the ground the angle of elevation of the top of the statue 60° and from the same point the angle of elevation of top of a pedestal is 45 degree find the height of the pedestal


Solution --- 0.8 (√3+1) m


Que 9 

Angle of elevation of top of a building from the foot of the tower is 30 degree and angle of elevation of the top of the tower from the foot of the building is 60 degree the tower is 50 m height find the height of the building

Solution -- 16⅔ m 


Que 10 

Two poles of equal heights are standing opposite each other on either side of the road which is 80m  wide  from a point between them on the road the angles of elevation of the top of the poles are 60 ° and 30 °respectively find the height of the pole  and the distance of the point from the pole


Solution--  20√3 m ,20 m ,60 m


Que 11

TV tower stands vertically on a bank of a canal from a point on the other bank directly opposite the tower the angle of elevation of the top of a tower is 60 ° from another point 20 away from this point on the line joining this point to the foot of the tower the angle of elevation of the top of the tower is 30 °find the height of the tower and the width of the canal

Solution -- 10√3 m ,10 m


Que 12 

The top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine the height of the tower

Solution -- 7(√3+1) m


Que 13 

As observed from the top of a 75 m high  lighthouse from the sea level the angles of depression of the two ships are 30° and 45° if one ship is exactly behind the other on the same side of the lighthouse find the distance between two ships

Solution --  75(√3-1) m


Que 14

1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground The angle of elevation of the balloon from the eyes of the girl at any instant is 60 ° after sometime angle of elevation reduces to 30 ° find the distance travelled by the balloon during the interval


Solution -- 58√3 m 


Que 15 

A straight highway leads to the foot of a tower in a standing at the top of a tower observes a car at an angle of depression of 30° which is approaching the foot of the tower with a uniform speed 6 seconds later angle of depression of the car is found to be 60 ° find the time taken by the car to reach the foot of the tower from this point

Solution -- 3 sec

Solution --







Thursday, November 11, 2021

Mock Test Series for class 10 --Maths

Sample paper for class 10 

CBSE Term 2 Maths 

Part 1



Part 2



Part 3







Que 1

Ratio of LCM and HCF of the least composite and least prime number is

a) 1:2

b) 2:1

c) 1:1

d) 1:3


Ans ( b) 







Que 2

The value of k for which the lines
  5x+7y= 3and  15x+21y = k coincide is 

a) 9

b) 5

c ) 7

d) 18

Ans (a)







Que 3

Girl walks 200 m east and then 150 m towards north the distance of the girl from the starting point is 

a) 350m

b) 250 m

c) 300 m

d) 225 m

Ans (b) 






Que 4

The length of the diagonals of a rhombus are 24 cm and 32 cm  then the length of the altitude of the rhombus is

a) 12 cm

b) 12.8 cm

c) 19 cm

d) 19.2 cm


Ans ( d ) 







Que 5

Two fair coins are tossed what is the probability of getting at the most one head

a) ¾

b) ¼

c) ½

d) ⅜


Ans (a) 




Que 6

∆ABC ~∆PQR If AM and PN are attitudes of∆ABC and ∆PQR  respectively. and
 AB²: PQ² = 4:9  then AM : PN 

a) 16:81

b) 4:9

c ) 3:2

d) 2:3

Ans ( d) 




Que 7

If 2sin²B-cos²B =2 then value of B is 

a) 0°

b) 90°

c) 45°

d) 30°

Ans ( b ) 





Que 8

Prime factors of the denominator of a rational number with the decimal expansion 44.1 23 are

a) 2,3

b) 2,3,5

c) 2,5

d) 3,5

Ans (c)





Que 9

The lines x=a and y= b are

a) intersecting

b) parallel

c) overlapping

d) none 

Ans (a)





Que 10

The distance of point A(-5,6) from the origin is 

a) 11 units

b) 61 units

c) √11 units

d) √61 units

Ans (d)




Que 11

If a²= 23/25 then a is 

a) rational

b) irrational

c) whole number

d) integer

Ans (b )





Que 12

If LCM (x,18) =36 and HCF (x,18) = 2 then x is 

a) 2

b) 3

c) 4

d) 5

Ans (c)





Que 13

In ∆ ABC right angled at B if tan A =√ 3 then cos A cosC - sin A sin C =

a) -1

b) 0

c) 1

d) √3/2

Ans (b)








Que 14

If the angles of ∆ABC are in ratio 1:1:2 (largest angle being angle C) then the value of  secA/cosec B - tan A/ cot B is 

a) 0

b)½

c) 1

d)√3/2

Ans (a)





Que 15

Number of revolutions made by a circular wheel of radius 0.7 m in rolling a distance of 176 m is

a) 22

b) 24

c) 75

d) 40

Ans (d )







Que 16

∆ABC is such that AB =3cm ,BC=2 cm ,
CA = 2.5 cm If ∆ ABC ~∆ DEF ,EF = 4 cm then perimeter of ∆DEF is 


a) 7.5cm 

b) 15 cm 

c) 22.5 cm

d) 30 cm


Ans (b) 

Solution




Que 17

If DE||BC ,AD= 3cm ,BD= 4cm and BC = 14 cm then DE equals 

a) 7 cm

b) 6 cm

c) 4 cm

d) 3cm



Ans  (b) 

Solution






Que 18

If 4tan B = 3, then 
(.4sinB-3cosB)/(4sinB +3cosB)

a) 0

b) ⅓

c) ⅔

d) ¾

Ans (a)

Solution





Que 19 

One equation of a pair of independent linear equation is   -5x+7y = 2 the second equation can be

a) 10x + 14y +4 = 0

b) -10 x- 14 y + 4  = 0

c) -10 x + 14 y + 4 = 0

d) 10x -14 y  = - 4


Que 20

Letter of English alphabet is chosen at random what is the probability that it is a letter of the word"MATHEMATICS"?

a) 4/13

b) 9/26

c) 5/13

d) 11/26

Ans (a)

Solution





Que 21

Sum of the two numbers is 12 15 their HCF is 81 then the possible number of pairs of such numbers are 

a) 2

b) 3

c) 4

d) 5


Que 22

Given  below is the graph representing two linear equations by the lines AB and CD respectively what is the area of the triangle formed by these two lines and the line x =0 


a) 3

b) 4

c) 6

d) 8




Ans (a)

Solution





Que 23

If tan A + cotA = 2 then tan²⁰ A+ cot²⁰ A.is 

a) 0

b) 2

c) 20

d) 2²⁰


Ans (b)

Solution




Que 24

If 217 x+ 131 y = 913 ,
131x+ 217 y = 827 then x+y is 

a) 5

b) 6

c) 7

d) 8


Ans  ( a )

Solution




Que 25

The LCM of two prime numbers p and q (p>q) is 221 .Find value of 3p-q

a) 4

b) 28

c) 38

d) 48


Que 26

A card is drawn from a well shuffled deck of cards what is the probability that the card drawn is neither or king nor queen

a) 11/13

b) 12/ 13

c) 11/26

d) 11/ 52

Que 27 

Two  fair dice are rolled simultaneously the probability that 5 will come up at least once is

a) 5/36

b)11/36

c) 12/36

d) 23/36

Que 28

1+sin²A = 3 sinAcosA  then values of cot A 

a) -1,1

b) 0,1

c) 1,2

d) -1,-1

Ans ( c )

Solution



Que 29

Vertices of a parallelogram in order are A(1,2),B(4,y),C(x,6) D(3,5) then (x,y) is 

a) (6,3)

b) (3,6)

c) (5,6)

d) ( 1,4)

Que 30

In the given figure ∆ACB =∆CDA ,AC = 8 cm ,AD = 3 cm then BD is 



a) 22/3

b) 26/ 3

c) 55/3

d) 64/3


Que. 31

Definition of the perpendicular bisector of a line segment joining points A( 4,5) and 
B( -2,3) is 

a) 2x -y +7 = 0

b) 3x + 2y -7 = 0

c) 3x - y- 7 = 0

d) 3x + y - 7 = 0

Ans ( d )

Solution






Que 32

In the given figure ,D is mid point of BC then value of cot y ° / cot x° is 

a) 2

b) 1/2

c) 1/3

d) 1/4


Ans ( a )

Solution




Que 33

Smallest number by which 1 /13 should be multiplied so that its decimal expansion terminates after two decimal places

a) 13/ 100

b) 13/ 10

c) 10/ 13

d) 100/13


Que 34

Side AB  and BE  of a right triangle right angled at B  are of lengths 16 cm and 8 cm respectively the length of the side of the largest square  FDGB  that can be inscribed in a triangle ABE is 


a) 32/3

b) 16/ 3

c ) 8/ 3

d) 4/ 3



Que 35

Point. P  divides the line segment joining 
R (-1,3)  and S( 9,8) in ratio k:1  if P lies on the line  x-y +2 =0 then value of k is

a) 2/3

b) 1/2

c) 1/3

d) 1/4

Ans ( a )

Solution




Que 36

In the figure given below ABCD is  square of side 14 cm  with E,F,G,H is the midpoints of the sides AB,BC,CD,DA  respectively the area of the shaded portion is


a) 44 

b) 49

c) 98

d) 49π/2


Que 37 

Given below is  the picture of the Olympic rings made by taking five congruent circles of radius 1 cm each  intersecting  in such a way that the chord formed by joining the point of intersection of two circles is also of length 1 cm the total area of all the dotted regions  assuming the thickness of the things to be negligible is




a) 4( π/12-√3/4)

b) (π/6-√3/4)

c) 4( π/6-√3/4)

d) 8(π/6-√3/4)

Ans ( d)

Solution




Que 38

If 2 and ½ are the zeros of px²+ 5x +r then 

a) p=r= 2

b) p=r= -2

c) p=2,r=-2

d) p=-2,r=2

An (b ) 

Solution




Que 39

Circumference of a circle is 100 cm the side of a square inscribed in a circle is

a) 50 √ 2 

b) 100/π

c) 50√2/π

d) 100√2/ π

Ans ( c )

Solution




Que 40

The number of solutions of 3^(x+y) = 243
243^(x-y) =3 is 

a) 0

b) 1

c) 2

d ) infinite


Que 41

The graph of the polynomial is given below

The zeros of polynomial are  

a) -3,-2,0,0

b) -2,0,2,0

c) -3,-2,0,2

d) -3,2,0,2

Solution (c) 

Solution---- 


Que 42

Find number of zeros of polynomial for given graph

a) 4

b) 2

c) 3

d) none

Solution




Que 43

Which of the following is not a quadratic polynomial


Solution-





Que 44

If 1  is the zero of the polynomial. 
3x² +5x + a  find the value of a 

a) -8

b) 8

c) 7

d). - 7

Solution






Que 45

A polynomial whose sum and product of zeros is 3 and 2. Find the equation of polynomial

a ) x²+3x+2

b) x²-3x-2

c) x²-3x + 2

d) none of these 


Solution--




Que 46

Find a quadratic polynomial whose zeros are 3 and 1/4 

a) 2x²+13x -3 = 0

b ) 4x² + 13 x +3 = 0

c ) 4x²-13 x -3 = 0

d) 4x² -13 x +3 = 0





Que 47

If 2 and 3 are the zeros of the polynomial 3x²-2kx+2m = 0 then value of k and m are 

a) 15,9/2

b) 15/2  ,- 9

c) 15/2,. 9

d ) none

Solution




Que 48

If a and b are the zeros of the equation 
x²-p(x+1)+ c = 0
Then ( a+1) ( b+1) = 0 then value of c is 

a ) -1

b) 1

c) 1/2

d) -1/2 

Solution



Part 49

If one zero of the polynomial 2x²- 5x -(2x+1) is twice the other zero then value of k 

a) 17/9

b) -17/9

c) 9/18

d) none

Solution






Monday, November 8, 2021

Ncert Solutions Class 10 Maths - Area Related to Circles

 Ncert Solutions Class 10 Maths - Area Related to Circles 


Mock Test Series

Que 1

Perimeter of the semicircular protractor is 36 cm find its diameter

a) 10 cm 

b) 12 cm 

c) 14 cm 

d) 15 cm 

Ans  ( c) 



Que 2

The the diameter of a circle whose area is equal to sum of area of two circles of diameter 16  cm and 12cm

a) 56 

b ) 42 

c) 28

d) 20 

Ans  ( d )




Que 3

The radii of two circles of 10 cm and 8cm find the radius of the circle which has circumference equal to sum of circumference of the two circles

a) 18 

b ) 36 

c ) 28

d) 14 

Ans  (a) 



Que 4

Circumference of a circle is 44 cm find the area of the circle

a) 276 cm²

b ) 44 cm²

c) 176 cm²

d) 154 cm²

Ans (d)


Que 5

Find area of sector of a circle of radius 10 cm which subtends an angle of 36° at centre 

a) 20π

b ) 10 π

c) πr²

d) 100 π


Ans  (b )





Exercise 12.1



Que
The radii of two circles are 19 cm and 9 cm find the radius of the circle whose circumference is equal to the sum of the circumference of the two circles

Solution




Que 2

The radii of two circles are 8cm and 6cm. Find the radius of the circle having area equal to sum of areas of two circles

Solution




Que 3

There is an archery target marked with its five scoring  regions from the centre outwards as gold ,red ,blue ,black and white .The diameter of the reason scoring gold is 21 cm and  each of other bands is of width 10.5 cm find the area of each regions

Solution




Que 4

The wheels of a car have a diameter of a 80 cm each.How many complete revolutions does each wheel make in 10 minutes when the car is traveling with a speed of 66 km / h

Solution 





Exercise 12.2 

Que 1

Find the area of a sector of a circle with radius 6 cm if angle of sector is 60 °

Solution




Que 2

Find the area of the quadrant of a circle having circumference is equal to 22 cm

Solution




Que 4

A chord of a circle of radius 10 cm subtends a right angle at the centre find the area of the minor segment and major sector

Solution





Que 10

An umbrella has 8 ribs which are equally spaced umbrella to be a flat circle of radius 45  cm find the area between two consecutive ribs of the umbrella

Solution



Que 11

A car  has two wipers which do not overlap
Each wiper has. blade of length 25 cm 
sweeping through an angle of 115° find total area cleaned at each  sweep of the blade 

Solution




Que 12 

To warn ships of underwater rocks light houses spread red coloured light over a sector of an angle 80°. To a distance of 16.5 km find the area of the sea over which ships are  warned

Solution




Que 13

A round table cover has six equal designs radius of the cover is 28 cm find cost of making designs at the rate of Rs  0.35  per cm²

Solution



Exercise 12.3 


Que 11




Que 9



Que 10




Que 12



Que 13









Tuesday, October 5, 2021

NCERT Solutions -Class 10 -Maths -Quadratic Equations

 NCERT Solutions -Class 10 

Quadratic Equations


Recorded Lectures

Lecture 1

How to write any quadratic equation the roots of the quadratic equations are given
P and Q are the two root of a quadratic equation then the equation is

x^2-(p+q)x+pq= 0





Discriminant method 

Most popular method in order to factorise a quadratic equation

Step 1 find discriminant using formula
b^2-4ac

Step 2
Find square root of discriminant value

Step 3 find value of x using formula

x. ={ -b+-√(b^2-4ac)}/2a

Note 
Value of discriminant is greater than zero then the roots are real and unequal

When value of discriminant is equal to zero then roots are real and equal 

Value of discriminant is less than zero then roots are imaginary we cannot factorise quadratic equation

Watch the lecture to solve different questions




Remainder Theorem

When we have equations  greater than power 2 ie of higher degrees then we use the remainder theorem in order to factorise the given quadratic equations
In order to understand step by step methods watch the whole lecture





NCERT solutions class 10th- Pair of Linear Equations in Two variables

 NCERT solutions class 10th- Pair of Linear Equations in Two variables


Solve Graphically
In a particular lecture explain how to solve the given linear equations in two variables by using graphs



after plotting and solving the equations
If Graph  contains two intersecting lines then it means that they have unique solution but if two lines are parallel then it has infinite solution




Consistent and Inconsistent Solution







Solution using Cramer Rule 



This is a mathematical method by which we solve linear equations in two variables cramer rule is the most popular method of solving linear equations what's the dash lecture in order to understand how to solve different questions using the cramer's rule


Ncert solutions exercise 3.2

Some of the  problems of exercise 3.2 are explained


Question on Boat 
In the lesson of linear equations in two variables we have different types of questions based on a stream and boat different method in order to solve these types of problems so in lecture attached below detail and most basic method as explain in order to solve the questions of your text book









Wednesday, September 8, 2021

NCERT solutions for class 10 Maths - Statistics and Probability

 Class 10th  Maths -

 

 Statistics and Probability


Sample Test Paper Term II 2022


Que 1--

If mean of 

7,10,4,12,x,3 is 7.5 find value of x

Que 2 ---

The marks obtained by students

14,11,23,14,18,7,8,5

 a) find mean 

b) find  mean if marks are increased by 5 marks


Que 3---

Marks obtained by 40 students

-------------------------------------------------------------------

Marks             Number of Students 

-------------------------------------------------------------------

5.                         6


6.                        A


7.                       16


8.                      13


9.                       B 

_____________________________________________

If mean is 7.2 find value of A and B


Que 4----

Find. Mean for given data 

____________________________________________

Class - Interval.                   Frequency


80--100.                                 20


100--- 120.                            30


120 -- 140                            20


140-- 160.                            40


160 -- 180.                             90

_____________________________________________



Que 5--  Find mean for following for data


Marks.                Number of  Students


11--20.                       2


21-- 30.                     6


31-- 40.                     10


41-- 50.                      12


51 -- 60.                     9 


61 - 70                       7


71 --80.                      4 

_____________________________________________


Que 6 ---


Find mean for following data


Life time (days).                   Number of bulbs


Less than 50                             70


Less than 100.                          21


Less than 150.                          52


Less than 200.                          79


Less than 250                          91


Less than 300.                          100


Que  7 ---


If mean is 24 find value of "A "


Marks.                           Number of students


0. --10.                                   7


10---20.                                  A


20-- 30.                                 8


30 --- 40                               10


40 --- 50.                                5


Que 8 ---


The median of the observations.

 11,12,14,18,(x+4), 30,32,35,41 is 24 find

 value of x 


Que 9 --- 

If 10,13,15,18,x+1,x+3,31,36,38,42 are observations with median 28 find value of x 


Que 10 --- 


For following frequency distribution find upper limit of median class


Class                      Frequency


0--5                            8


5--10.                        10 


10--- 15.                     19 


15--20.                       25


20-- 25                       8 


Que 11


Draw a less than ogive graph for following frequency distribution


Class.                                Frequency


0---10                                      7


10 ---20.                                  14


20--30.                                    13


30-- 40                                    12


40--50                                     20


50 -- 60                                   11


60 --- 70                                   15


70 -. 80                                     8


Que 12--- 

Following table shows the age of patients admitted in  hospital find the mode


Age.                             Number of Patients


5--15.                             60


15---25.                         110


25 -- 35                          210


35-- 45.                          230


45-- 55                           150


55--65.                             50 



Que 13 --- 

Draw MORE  than  ogive graph for following data


Weight (kg)                  Number of Students


40---44.                                 4


44--- 48.                               10


48---- 52.                              30


52--- 56.                                24


56--- 60.                                 18


60 ---- 64.                              12


64--- 68.                                2


In order to solve above questions watch the attached lectures given below

How do we find the class limit and what is the lower limit and upper limit in a class how to find the class mark and class boundary for a statistics data what is class size and how do we find the cumulative frequency of a data





Statistics

Mean =

Sum of observations/number of 

observations









For solution watch the lecture ---




Median


When total number of observations is odd

Median = l+{(n/2-cuf)/f}*h


Question---








Solution ----





How to draw ogive graph---


FOR  LESS  than --

Question---





Solution----




For  MORE than


Question





Solution---





The different topics explain in the given lecture

Different methods to find the mean of the data all the methods are explain in the attach lecture

How to find the median of the data if the number of data are odd and the number of data is even

How to find the mode of a given statistical data







Probability


Formula for the probability

Number of favourable sample spaces/total number of sample spaces


P(A)+P(B) =1





Problems based on card


Find The probability of 

a) an ace

b) black queen

c)  jack of a spade 

d) 5 of a red suite

e ) face card

f ) either king or a queen

g ) neither a king nor a queen



Problems based on ball and boxes

 lecture contains how to find the probability whenever then there are some objects on balls are kept in a boxes or a bag

Type 1 
A bag  contains 4 green and 6 black and 7  white balls
Find the probability
a) there is either green or black balls

b ) either green or white balls

c ) neither green nor black balls

Type 2

There are 40 balls in a box in which 10 balls are white 16 balls are red and rest of the balls are black find the probability of the

a) white balls 

b) red balls

c) black balls

d) not a black ball

e) not a red ball




Questions on dice(single)

The questions on the single dice throw explain in the given lecture by taking one example

Question
A dice is thrown once find the probability of

a) getting 5

b) getting 7

c) a number 5 or 6 

d ) a number between 3 and 6

e ) a number greater than 3

f ) a number less than 3

g ) odd number


Questions and solutions on pair of dice
 
Lecture contains what are the sample spaces when two dice are thrown
The question which I explain in this particular lecture is given below

If two dice are thrown simultaneously find the probability

a) even number as a sum on the two dice

b) a total of 10 on the two dice

c) not a total of 10

d) doublet

e) multiple of 2 on the first die and number  6 on the other die




NCERT solutions for class 10th Maths -Surface Areas and Volume

 NCERT solutions for class 10th  Maths - Surface Areas and Volumes


Surface area and volume of cone






NCERT solutions for class 10th Maths -Trignometry

 Trigonometry


The word trigonometry means measurement of triangles in a right angle triangle the side opposite to the acute angle is called perpendicular and side adjustment is called base and side opposite to the right angle is called hypotenuse the ratio between the length of pair of two sides of right angle triangle is called a grammatical ratio there are 16 vertical ratios sine cosine tangent cotangent  secant and cosecant

Introduction

This particular video explain different formulas of trigonometric ratios cos theta sin theta tan theta sec theta cos theta

Value of one of them is given how we find the value of all other six technometry ratios is explained in this particular video


Trignometrical Ratios

Lecture 1

Topic Covered


What are six trigonometry ratios and what are their formula

Sin A = perpendicular/Hypotenuse

Cos A = Base /Hypotenuse

Tan A = perpendicular/Base

Cot A = Base/perpendicular

Sec A = 1/Cos A = Hypotenuse / Base

Cosec A = 1/sin A 

= Hypotenuse / perpendicular

Watch the lecture how to learn and derive it 


Lecture 2 

Questions discussed in lecture attached below are 

If cos A = 5/13

Find 

(sinA- cot A)/ 2 tan A

Type 4

If 4 cot A = 3 

Find  sec A and cosec²A - cot²A

Type 5

If cot A = 1

Find 

5tan²A + 2sin²A-3



Lecture 3

Topic Covered in lecture attached below 

If ABC is right angled triangle at B if 
AB =3cm ,BC = 4cm ,AC = 5cm 

Find

Sin A

Sin C

Cos A 

Cos C 

Tan C 



Lecture 4 

Topic Covered

Trigonometry ratios of standard angles

How to convert angles which are in degree into radians

Convert 30°

Convert 120°

How to convert angles which are given in radians into degrees

π/6

5π/3

Explanation how to solve the questions of the relation ship between angle ,arc and the radius of the circle

Que-- A needle  of length 7 m moves  from 5 minute to 15 minutes find how much distance is it covers and what angle does this needle makes

Find the value of 

tan 120°

sin 210°

cos 570°

sec. 350°

cot 2010°



Lecture 5

How to find value of cos 870 ° 

Step 1

Divide 870 with 360(2π)

Step 2

Cos (2π+150°)

Step 3

Cos 150°

Step 4

Cos (π-30°)

Step 5

- cos 30°

-√3/2




Lecture 6

Exercise 8.4 NCERT solutions CBSE Board class 10

Questions discussed are

1) (cosec A- cot A)²= (1-cosA)/(1+cos A)

2) cos A/( 1+ sin A).+ (1+sin A)/cos A = 2sec A

3) (1+sec A) / sec A = sin²A/ 1- cos A

4) √( 1+sin A) / (1-sin A). = Sec A + tan A

5) ( cos A- sin A+ 1)/(cos A+sin A+ 1). 
 = cosec A + cot A





Lecture 7 in

Exercise 8.4 

Question discussed are

(sin²63°+sin²27°)/(cos²17°+cos²73°)

sin 25°cos 65°+ cos 25° sin 65 °






Application of Trigonometry



All the textbook questions of CBSE board of class 10th of the lesson application of trigonometry is explained










Extra questions


Trigonometry(त्रिकोणमिति)

Lecture 1


Questions discussed


1) cos 2π/3


2) cotA/2 = x 


3) sin 11π/6


4) 1/(tan A+ cot A) = x


5) cot A/ √(1+cot²A) = x


6) √(1-cosA)/(1+cosA)


7) sec 225°


8) tan π/3 + cosec π/6


9) cot A = x


10) cosec A= 1.25


Find 

(4tan A - cos A)/(16 sec A - cot A)




Lecture 2


How to convert angles which are in degree into radians

Convert 30°

Convert 120°

How to convert angles which are given in radians into degrees

π/6

5π/3

Explanation how to solve the questions of the relation ship between angle ,arc and the radius of the circle

Que-- A needle of length 7 m moves from 5 minute to 15 minutes find how much distance is it covers and what angle does this needle makes

Find the value of 

tan 120°

sin 210°

cos 570°

sec. 350°

cot 2010°




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