Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(C)

Question 1

Show that:

(i) 

(ii) 

(iii) 

Solution 1

(i)

(ii)

(iii)

Question 2

Express each of the following in terms of angles between 0°and 45°:

(i) sin 59°+ tan 63°

(ii) cosec 68°+ cot 72°

(iii)cos 74°+ sec 67°

Solution 2

Question 3

Show that:

(i) 

(ii) 

Solution 3

(i) 

(ii) 

Question 4

For triangle ABC, show that:

(i) 

(ii) 

Solution 4

(i) We know that for a triangle ABC

  A + B + C = 180°

(ii) We know that for a triangle ABC

 A + B + C = 180°

B + C = 180° - A

Question 5

Evaluate:

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

(vii) 

(viii) 

(ix) 

Solution 5

(i)

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

(vii) 

(viii) 

(ix) 

Question 6

A triangle ABC is right angled at B; find the value of 

Solution 6

Since, ABC is a right angled triangle, right angled at B.

So, A + C = 90

Question 7

Find (in each case, given below) the value of x if:

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

(vii) 

Solution 7

(i) 

Hence, x = 

 

(ii) 

Hence, x = 

 

(iii) 

Hence, x = 

 

(iv) 

Hence, x = 

 

(v) 

Hence, x = 

 

(vi) 

Hence, x = 

 

(vii) 

Hence, 

Question 8

In each case, given below, find the value of angle A, where 

(i) 

(ii) 

Solution 8

(i) 

(ii) 

Question 9

Prove that:

(i) 

(ii) 

Solution 9

(i)

(ii)

Question 10

Evaluate :

Solution 10

Question 11

Evaluate

sin² 34° + sin² 56° + 2tan 18° tan72° - cot² 30°

Solution 11

Question 12

Without using trigonometrical tables, evaluate:

Solution 12