## Book: NCERT - Mathematics

### Chapter: 8. Introduction to Trigonometry

#### Subject: Maths - Class 10th

##### Q. No. 4 of Exercise 8.2

Listen NCERT Audio Books - Kitabein Ab Bolengi

4
##### 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°

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

Let A = 30° and B = 60°

sin (A + B) = sin (30° + 60°)

= sin 90°

= 1

sin A + sin B = sin 30° + sin 60°

=

=

Clearly, sin (A + B) ≠sin A + sin B

Hence, the given statement is false

(ii) The value of sin θ increases as θ increases in the interval of 0° < θ < 90° as sin 0° = 0

sin 30o =

sin 45o = = 0.707

sin 60o = = 0.886

sin 90° = 1

Hence, the given statement is true

(iii) cos 0° = 1

cos 30o =

cos 45o =

cos 60o =

cos 90° = 0

It can be observed that the value of cos θ does not increase in the interval of 0° < θ < 90°

Hence, the given statement is false

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

This is true when θ = 45°

As,

sin 45o =

cos 45o =

It is not true for all other values of θ

As sin 30o = and cos 30o =

Hence, the given statement is false

(v) cot A is not defined for A = 0°

cot A =

cot 0o =

= =undefined

Hence, the given statement is true

4

1
2
2
2
2
3
4