If cot (α + β) = 0,

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

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