# State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B.

(ii) The value of sin θ increases as θ increases.

(iii) The value of cos θ increases as θ increases.

(iv) sin θ = cos θ for all values of θ.

(v) cot A is not defined for A = 0°.

**Solution:**

We will use the basic definitions of trigonometric ratios to solve the given problem.

(i) sin (A + B) = sin A + sin B.

For the purpose of verification, Let A = 30° and B = 60°

L.H.S = sin (A + B)

= sin (30° + 60°)

= sin 90°

= 1

R.H.S = sin A + sin B

= sin 30° + sin 60°

= 1/2 + √3/2

= (1 + √3)/2

Since, sin (A + B) ≠ sin A + sin B.

Hence, the given statement is false.

(ii) The value of sin θ increases from 0 to 1 as θ increases from 0° to 90°

sin 0° = 0

sin 30° = 1/2 = 0.5

sin 45° = 1/√2 = 0.707

sin 60° = √3/2 = 0.866

sin 90° = 1

Hence, the given statement is true.

(iii) The value of cos θ decreases from 1 to 0 as θ increases from 0° to 90°

cos 0° = 1

cos 30° = √3/2 = 0.866

cos 45° = 1/√2 = 0.707

cos 60° = 1/2 = 0.5

cos 90° = 0

Hence, the given statement is false.

(iv) sin θ = cos θ for all values of θ, this is true when θ = 45°

As sin 45° = 1/√2 and cos 45° = 1/√2

It is not true for other values of θ

sin 30° = 1/√2 and cos 30° = √3/2

sin 60° = √3/2 and cos 60° = 1/√2

sin 90° = 1 and cos 90° = 0

Hence, the given statement is false.

(v) cot A = cos A/sin A

cot 0° = cos 0°/sin 0° = 1/0 = undefined

Hence, the given statement is true.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 8

**Video Solution:**

## State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B. (ii) The value of sin θ increases as θ increases. (iii) The value of cos θ increases as θ increases. (iv) sin θ = cos θ for all values of θ. (v) cot A is not defined for A = 0°

Maths NCERT Solutions Class 10 Chapter 8 Exercise 8.2 Question 4

**Summary:**

The statements (i) sin (A + B) = sin A + sin B, (iii) The value of cos θ increases as θ increase, (iv) sinθ = cosθ for all values of θ are false and the statements (ii) The value of sin θ increases as θ increases , and (v) cot A is not defined for A = 0° are true.

**☛ Related Questions:**

- Evaluate the following: (i) sin 60° cos 30° + sin 30° cos 60° (ii) 2 tan² 45° + cos² 30° - sin² 60° (iii) cos 45°/(sec 30° + cosec 30°) (iv) sin 30° + tan 45° - cosec 60°/(sec 30° + cos 60° - cot 45°)
- Choose the correct option and justify your choice:(i) 2 tan 30°/1 + tan2 30°(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 60°(ii) 1 - tan2 45°/1 + tan2 45°(A) tan 90° (B) 1 (C) sin 45° (D) 0°(iii) sin 2A = 2 sin A is true when A =(A) 0° (B) 30°(C) 45° (D) 60°(iv) 2 tan 30°/1 - tan2 30°(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°
- If tan (A + B) = √3 and tan (A - B) = 1/√3; 0° < (A + B) ≤ 900 , A > B, find A and B.

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