Is it right to say that sin(A + B) = Sin A + Sin B? Justify your answer.

No, it is not correct to say that sin (A + B) = sin A + sin B.

Justification: Let’s justify it by showing contradiction.

Let it be true that, sin (A + B) = sin A + sin B.

Now, let A = 30° and B = 60°

Then,

sin (30° + 60°) = sin 30° + sin 60°

⇒ sin 90° = sin 30° + sin 60°

⇒ 1 = 1/2 + √3/2

⇒ 1 = (1 + √3)/2

But, it’s not true.

1 ≠ (1 + √3)/2

Hence, we have a contradiction.

And therefore, it’s not right to say that sin (A + B) = sin A + sin B.