If ( + )=0, then ( +2 ) is equal to: 1. 2. 2 3. 4. 2 - Vidyadip

Question

If $\cot(\alpha+\beta)=0,$ then $\sin(\alpha+2\beta)$ is equal to:

$\sin\alpha$
$\cos2\beta$
$\cos\alpha$
$\sin2\alpha$

✓

Answer

$\sin\alpha$

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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