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Trigonometry — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometry2 Marks
Question
Solve: $2 \cos ^2 \theta+\sin \theta-2=0$.
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Answer

$2 \cos 2 \theta+\sin \theta-2=0$
$\Rightarrow 2\left(1-\sin ^2 \theta\right)+\sin \theta-2=0$
$\Rightarrow 2-2 \sin ^2 \theta+\sin \theta-2=0$
$\Rightarrow-\sin \theta(2 \sin \theta-1)=0$
$\Rightarrow \sin \theta(2 \sin \theta-1)=0$
$\Rightarrow \sin \theta=0 \text { or } 2 \sin \theta-1=0$
$\Rightarrow \sin \theta=0 \text { or } \sin \theta=\frac{1}{2}$
$\Rightarrow \theta=30^{\circ}$

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