Find the acute angle such 2cos^2 = 3sin θ. - Vidyadip

Question

Find the acute angle $\theta $ such $2cos^2 \theta = 3sin θ$.

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Answer

$2 \cos ^2 0=3 \sin \theta$
$\therefore 2\left(1-\sin ^2 \theta\right)=3 \sin \theta$
$\therefore 2-2 \sin ^2 \theta=3 \sin \theta$
$\therefore 2 \sin ^2 \theta+3 \sin 9-2=\theta$
$\therefore 2 \sin ^2 \theta+4 \sin \theta-\sin \theta-2=\theta$
$\therefore 2 \sin \theta(\sin \theta+2)-1(\sin \theta+2)=\theta$
$\therefore(\sin \theta+2)(2 \sin \theta-1)=0$
$\therefore \sin \theta+2=0 \text { or } 2 \sin \theta-1=0$
$\therefore \sin \theta=-2 \text { or } \sin \theta=1 / 2$
$\text { Since, }-1 \leq \sin \theta \leq 1$
$\therefore \sin \theta=1 / 2$
$\therefore \theta=30^{\circ} \ldots[\because \sin 30=1 / 2]$

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