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8. Introduction to Trigonometry
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If $2 \sin ^{2} \theta-\cos ^{2} \theta=2$, then find the value of $\theta$.
A
$30^{\circ}$
B
$90^{\circ}$
C
$0^{\circ}$
D
$120^{\circ}$
Solution
Given, $2 \sin ^{2} \theta-\cos ^{2} \theta=2$
$2 \sin ^{2} \theta-\left(1-\sin ^{2} \theta\right)=2$ $\left[\because \sin ^{2} \theta+\cos ^{2} \theta=1\right]$
$2 \sin ^{2} \theta+\sin ^{2} \theta-1=2$
$3 \sin ^{2} \theta=3$
$\sin ^{2} \theta=1$ $\left[\because \sin 90^{\circ}=1\right]$
$\sin \theta=1=\sin 90^{\circ}$
$\theta=90^{\circ}$
Standard 10
Mathematics
