Question

State whether the following is true or false. Justify your answer.

sin (A + B) = sin A + sin B

Options

• True

• False

Answer 1

This statement is False.

Explanation:

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°

= `1/2 + (sqrt3)/2`

= `(1+sqrt3)/2`

Clearly, sin (A + B) ≠ sin A + sin B

Hence, the given statement is false.