If \( 15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6 \), for some \( \al...

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If \( 15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6 \), for some \( \alpha \in R \), then the value of \( 27 \sec ^{6} \alpha+8 \operatorname{cosec}^{6} \alpha \) is equal to:
\( \mathrm{P} \)
[JEE Main-2021 (February)]
W)
(a) 350
(b) 500
(c) 400
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