If 1-cos theta = sin theta cdot sin frac{thet | vedclass

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(C) Given equation: $1 - \cos 	heta = \sin 	heta \cdot \sin \frac{	heta}{2}$ Using the identity $1 - \cos 	heta = 2 \sin^2 \frac{	heta}{2}$ and $

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$2n\pi, 4n\pi, n \in Z$

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(C) Given equation: $1 - \cos 	heta = \sin 	heta \cdot \sin \frac{	heta}{2}$ Using the identity $1 - \cos 	heta = 2 \sin^2 \frac{	heta}{2}$ and $\sin 	heta = 2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}$,we get: $2 \sin^2 \frac{	heta}{2} = (2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}) \cdot \sin \frac{	heta}{2}$ $2 \sin^2 \frac{	heta}{2} = 2 \sin^2 \frac{	heta}{2} \cos \frac{	heta}{2}$ $2 \sin^2 \frac{	heta}{2} (1 - \cos \frac{	heta}{2}) = 0$ Case $1$: $\sin^2 \frac{	heta}{2} = 0 \implies \frac{	heta}{2} = n\pi \implies 	heta = 2n\pi$ Case $2$: $1 - \cos \frac{	heta}{2} = 0 \implies \cos \frac{	heta}{2} = 1 \implies \frac{	heta}{2} = 2n\pi \implies 	heta = 4n\pi$ Combining both,the solution is $	heta = 2n\pi$ or $	heta = 4n\pi$ for $n \in Z$.

If $1-\cos \theta = \sin \theta \cdot \sin \frac{\theta}{2}$,then the value of $\theta$ is

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