Question:
If cot (α + β) = 0, sin (α + 2β) is equal to
(a) sin α
(b) cos 2 β
(c) cos α
(d) sin 2 α
Solution:
(a) sin α
Given:
$\cot (\alpha+\beta)=0$
$\Rightarrow \frac{\cos (\alpha+\beta)}{\sin (\alpha+\beta)}=0$
$\Rightarrow \cos (\alpha+\beta)=0$
$\Rightarrow \alpha+\beta=\frac{\pi}{2}$
Therefore, $\sin (\alpha+2 \beta)=\sin (\alpha+\alpha+\beta)$
= sin α