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If $\sin \theta+\operatorname{cosec} \theta=4$, then $\sin ^2 \theta+\operatorname{cosec}^2 \theta=$
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Verified Answer
The correct answer is:
$14$
We have, $\sin \theta+\operatorname{cosec} \theta=4$
$\Rightarrow \frac{1}{\operatorname{cosec} \theta}+\operatorname{cosec} \theta=4$
Squaring both sides,
$\frac{1}{\operatorname{cosec}^2 \theta}+\operatorname{cosec}^2 \theta+2=16$
$\Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta=16-2=14$
$\Rightarrow \frac{1}{\operatorname{cosec} \theta}+\operatorname{cosec} \theta=4$
Squaring both sides,
$\frac{1}{\operatorname{cosec}^2 \theta}+\operatorname{cosec}^2 \theta+2=16$
$\Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta=16-2=14$
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