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If $\sin x+\operatorname{cosec} x=3$, then value of $\sin ^{4} x+\operatorname{cosec}^{4} x$ is
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The correct answer is:
47
We have $\sin x+\operatorname{cosec} x=3$
$\therefore \sin ^{2} x+\operatorname{cosec}^{2} x+2 \sin x \operatorname{cosec} x=9$
$\therefore \sin ^{2} x+\operatorname{cosec}^{2} x=9-2=7$
$\therefore \sin ^{4} x+\operatorname{cosec}^{4} x+2 \sin ^{2} x \operatorname{cosec}^{2} x=49$
$\therefore \sin ^{4} x+\operatorname{cosec}^{4} x=49-2=47$
$\therefore \sin ^{2} x+\operatorname{cosec}^{2} x+2 \sin x \operatorname{cosec} x=9$
$\therefore \sin ^{2} x+\operatorname{cosec}^{2} x=9-2=7$
$\therefore \sin ^{4} x+\operatorname{cosec}^{4} x+2 \sin ^{2} x \operatorname{cosec}^{2} x=49$
$\therefore \sin ^{4} x+\operatorname{cosec}^{4} x=49-2=47$
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