Can sin(A+B)= sin⁡ A+sin⁡ B?

Question

Is it ever possible that sin(A+B)= sin⁡ A+sin⁡ B? If so, explain how. If not, explain why not.

Answer 1

But note that, for most values of A and B, sin(A+B) does NOT equal sin A + sin B.

(Try A and B of 90 degrees, for example).

That is, sin(A+B) = sin A + sin B is NOT a trig identity.

Another quick way to determine whether this is a trig identity or not is to note that the range of sin(A+B) is [-1,1], but the range of sin A + sin B is [-2,2].

Answer 2

sin (0° + 90°) = sin 0° + sin 90°