If 2 ^2 + 3sin = 0, find the permissible values of cosθ. - Vidyadip

Question

If $2\sin^2 \theta + 3sin \theta = 0$, find the permissible values of cosθ.

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Answer

$2 \sin { }^2 \theta+3 \sin \theta=0$
$\therefore \sin \theta(2 \sin \theta+3)=0$
$\therefore \sin \theta=0 \text { or } \sin \theta=\frac{-3}{2}$
$\text { Since }-1 \leq \sin \theta \leq 1,$
$\sin \theta=0$
$\sqrt{1-\cos ^2 \theta}=0 \ldots\left[\because \sin ^2 \theta=1-\cos ^2 \theta\right]$
$\therefore 1-\cos ^2 \theta=0$
$\therefore \cos ^2 \theta=1$
$\therefore \cos \theta= \pm 1 \ldots[\because-1 \leq \cos \theta \leq 1]$

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