Question

Prove that sin( A+B )= sin A + sin B

Answer 1

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

Solution : False Because

When A = 60° and B = 30°. Then,

sin (A + B) = sin (60° + 30°) = sin 90° = 1

and, sin A + sin B = sin 60° + sin 30°

                             = $\frac{\sqrt{3}}{2} + \frac{1}{2}$

                             = $\frac{\sqrt{3}+1}{2}$

⇒ sin (A + B) ≠ sin A + sin B