Question

Does it hold or not?

$\sin (A+B)=\sin A+\sin B$ for $A={30}^o,B={60}^o$.

Answer 1

For $A={30}^o,B={60}^o$.

Then $A+B={90}^o$.

Then $\sin (A+B)$

$=\sin {90}^o$

$=1$ ......(1).

Again

$\sin A+\sin B$

$=\sin {30}^o+\sin {60}^o$

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

$=\frac{1+\sqrt{3}}{2}$ ......(2).

It is clear from (1) and (2) that equality does not hold for the given values of

$A$ and $B$.