Question
If $\cot(\alpha+\beta)=0,$ then $\sin(\alpha+2\beta)$ is equal to:
- $\sin\alpha$
- $\cos2\beta$
- $\cos\alpha$
- $\sin2\alpha$
Solution:
Given:
$\cot(\alpha+\beta)=0$
$\Rightarrow\frac{\cos(\alpha+\beta)}{\sin(\alpha+\beta)}=0$
$\Rightarrow\cos(\alpha+\beta)=0$
$\Rightarrow\alpha+\beta=\frac\pi2$
$\therefore\sin(\alpha+2\beta)=\sin(\alpha+\alpha+\beta)$
$=\sin\alpha$
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