Number of solution(s) of the equation sin 2th | vedclass

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Question

${\sin 2 	heta+\cos 2 	heta=-\frac{1}{2}} $

${\sin \left(\frac{\pi}{4}+2 	hetaight)=-\frac{1}{2 \sqrt{2}}} $

${	ext { Let } \frac{\pi}{4}+

Vedclass · Accepted Answer

$1$

Vedclass · Answer

${\sin 2 	heta+\cos 2 	heta=-\frac{1}{2}} $

${\sin \left(\frac{\pi}{4}+2 	hetaight)=-\frac{1}{2 \sqrt{2}}} $

${	ext { Let } \frac{\pi}{4}+2 	heta=\alpha} $

${\sin \alpha=-\frac{1}{2 \sqrt{2}}} $

${	herefore 	ext { only one solution }}$

Number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ is-

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