If sin 2theta = cos theta and 0

Question

(D) Given $\sin 2	heta = \cos 	heta$. Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$,we have: $2 \sin 	heta \cos 	heta = \cos 	het

Vedclass · Accepted Answer

$90^o, 30^o, 150^o$

Vedclass · Answer

(D) Given $\sin 2	heta = \cos 	heta$. Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$,we have: $2 \sin 	heta \cos 	heta = \cos 	heta$ $2 \sin 	heta \cos 	heta - \cos 	heta = 0$ $\cos 	heta (2 \sin 	heta - 1) = 0$ This implies either $\cos 	heta = 0$ or $2 \sin 	heta - 1 = 0$. Case $1$: $\cos 	heta = 0$. Since $0 Case $2$: $2 \sin 	heta - 1 = 0 \Rightarrow \sin 	heta = \frac{1}{2}$. Since $0 Thus,the possible values of $	heta$ are $30^o, 90^o, 150^o$.

If $\sin 2\theta = \cos \theta$ and $0 < \theta < \pi$,then the possible values of $\theta$ are:

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