Question

Question 4 (i)
State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.

Answer 1

(i) False.
Let $A={30}^{\circ }$ and $B={60}^{\circ }$, then
L.H.S.:
$sin(A+B)=sin({30}^{\circ }+{60}^{\circ })=sin{90}^{\circ }=1$
R.H.S.:
$sinA+sinB=sin{30}^{\circ }+sin{60}^{\circ }$
$=\frac{1}{2}+\frac{\sqrt{3}}{2}$
L.H.S. $\ne$ R.H.S. Therefore, the given statement is false.