First slide

Compound angles

Question

If $\cot (α + β) = 0, then \sin (α + 2 β)$ can be

Moderate

A

$\sin β$
B

$- \sin α$
C

$\cos α$
D

$\cos β$

Solution

$\begin{array}{l} \cot (α + β) = 0 \Rightarrow \cos (α + β) = 0 \\ \Rightarrow \sin (α + 2 β) = \sin (α + β) \cos β + \sin βcos (α + β) \\ = \pm \cos β (∵ \sin (α + β) = \pm 1) \end{array}$

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