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The solution of the equation $1 - \cos θ = \sin θ \sin \frac{θ}{2}$ is

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a

n π, n \in Z

b

2 n π, n \in Z

c

\frac{n π}{2}, n \in Z

d

none of these

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detailed solution

Correct option is B

We have

$\begin{array}{l} 1 - \cos θ = \sin θ \sin \frac{θ}{2} \\ \Rightarrow 2 \sin^{2} \frac{θ}{2} = 2 \sin^{2} \frac{θ}{2} \cos \frac{θ}{2} \\ \Rightarrow 2 \sin^{2} \frac{θ}{2} (1 - \cos \frac{θ}{2}) = 0 \\ \Rightarrow \sin \frac{θ}{2} = 0, \cos \frac{θ}{2} = 1 \end{array}$

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