If $2 \sin ^{2} x+7 \cos x=5$, then permissible value of $\cos x$ is

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Aicharya · Accepted Answer

We have $2 \cos ^{2} 	heta+3 \cos 	heta=2$ $2 \cos ^{2} 	heta+4 \cos 	heta-\cos 	heta-2=0 \Rightarrow 2 \cos 	heta(\cos 	heta+2)-1(\cos 	heta+2)=0$ $(2 \cos 	heta-1)(\cos 	heta+2)=0$ $	herefore \cos 	heta=\frac{1}{2},-2$ (Impossible) $\Rightarrow \cos 	heta=\frac{1}{2}$

If $2 \sin ^{2} x+7 \cos x=5$, then permissible value of $\cos x$ is

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