The sum of all values of theta in[0,2 pi] sat | vedclass

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Question

$2 \sin ^2 	heta=\cos 2 	heta$
$2 \sin ^2 	heta=1-2 \sin ^2 	heta$
$4 \sin ^2 	heta=1$
$\sin ^2 	heta=\frac{1}{4}$
$\sin 	heta= \pm \frac{1

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

$2 \sin ^2 	heta=\cos 2 	heta$
$2 \sin ^2 	heta=1-2 \sin ^2 	heta$
$4 \sin ^2 	heta=1$
$\sin ^2 	heta=\frac{1}{4}$
$\sin 	heta= \pm \frac{1}{2}$
$2 \cos ^2 	heta=3 \sin 	heta$
$2-2 \sin 2 	heta+3 \sin 	heta-2=0$
$(2 \sin 	heta-1)(2 \sin 	heta-2)=0$
$\sin 	heta=\frac{1}{2}$
so common equation which satisfy both equations is $\sin 	heta=\frac{1}{2}$
$	heta=\frac{\pi}{6}, \frac{5 \pi}{6} \quad(	heta \in[0,2 \pi])$
$\operatorname{Sum}=\pi$

The sum of all values of $\theta \in[0,2 \pi]$ satisfying $2 \sin ^2 \theta=\cos 2 \theta$ and $2 \cos ^2 \theta=3 \sin \theta$ is

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