# R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 5 – Trigonometric Ratios

## Chapter 5 – Trigonometric Ratios Exercise Ex. 5

Question 1

If , find the values of all T-ratios of .

Solution 1

Given:

Let us draw a ABC in which B = 90o and BAC =

Question 2

If , find the values of all T-ratios of

Solution 2

Let us draw a ABC in which B = 90o and BAC =

By Pythagoras theorem, we have

Question 3

Solution 3

Question 4

If cot = 2, find the values of all T-ratios of .

Solution 4

Question 5

If find the values of all T-ratios of .

Solution 5

Let us draw a ABC in which B = 90o and BAC =

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

If cos  = 0.6, show that (5 sin  – 3 tan ) = 0.

Solution 9

Given:

Let us draw a triangle ABC in which B = 90o and A =

Question 10

If show that

Solution 10

Let us draw a ABC in which B = 90o and A =

Question 11

If show that

Solution 11

Let us draw a ABC in which B = 90o and A =

Question 12

If show that

Solution 12

Given:

Let us draw a triangle ABC in which B = 90o and A =

By Pythagoras theorem, we have

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

If show that

Solution 18

Let us draw a ABC in which  B = 90o and BAC =

Question 19

If show that

Solution 19

Given:

Let us draw a triangle ABC in which B = 90o and A =

By Pythagoras theorem, we have

Question 20

Solution 20

Question 21

If 3 cot  = 2, show that

Solution 21

Given:

Let us draw a triangle ABC in which B = 90o and A =

By Pythagoras theorem, we have

Question 22

Solution 22

Question 23

If verify that

Solution 23

Given:

Let us draw a triangle ABC in which B = 90o and A =

By Pythagoras theorem, we have

Question 24

In
the adjoining figure, ∠B =90°, ∠BAC
0,
BC = CD = 4 cm and AD = 10 cm. Find (i) sin θ
and (ii) cos θ.

Solution 24

Question 25

In a ABC, it Is given that B = 90o, AB = 24 cm and BC = 7cm.

Find the value of (i) sin A(ii) cos A(iii) sin C(iv) cos C.

Solution 25

Given: ABC in which B = 90o, AB = 24 cm and BC = 7cm

By applying Pythagoras theorem

(i)For  T-ratio of A , we have

Base AB= 24cm

Perpendicular BC = 7cm

Hypotenuse AC = 25cm

(ii)For T-ratio of C , we have

Base BC = 7 cm

Perpendicular AB= 24cm

Hypotenuse AC = 25cm

Question 26

Solution 26

Question 27

In
a ∆ABC,
∠B
= 900, AB = 12 cm and BC = 5 cm.

Find
(i) cos A (ii) cosec A
(iii) cos C (iv) cosec C.

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

If
∠A
and ∠B
are acute angles such that sin A = sin B then prove that ∠A
= ∠B.

Solution 30

Consider two right triangles XAY and WBZ such that sin A = sin B

Question 31

If
∠A
and ∠B
are acute angles such that tan A = tan B then prove that ∠A
= ∠B.

Solution 31

Consider two right triangles XAY and WBZ such that tan A = tan B

Question 32

In
a right ∆ABC, right-angled at B, if tan A = 1
then verify that 2 sin A. cos A = 1.

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

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