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

Answer 1

(a) $\sin \alpha$


$$\begin{gathered} \text{Given:} \\ \cot (\alpha +\beta )=0 \\ \Rightarrow \frac{\cos (\alpha +\beta )}{\sin (\alpha +\beta )}=0 \\ \Rightarrow \cos (\alpha +\beta )=0 \\ \Rightarrow \alpha +\beta ={\displaystyle \frac{\mathrm{\pi }}{2}} \end{gathered}$$
^{$$\begin{gathered} \mathrm{Therefore},\sin \left(\alpha +2\beta \right)=\sin \left(\alpha +\alpha +\beta \right) \\ =\sin \alpha \end{gathered}$$}