If $\sin x+\operatorname{cosec} x=3$, then value of $\sin ^{4} x+\operatorname{cosec}^{4} x$ is

If $\sin x+\operatorname{cosec} x=3$, then value of $\sin ^{4} x+\operatorname{cosec}^{4} x$ is
  1. 74
  2. 47
  3. 07
  4. 49

Solution

We have $\sin x+\operatorname{cosec} x=3$ $\therefore \sin ^{2} x+\operatorname{cosec}^{2} x+2 \sin x \operatorname{cosec} x=9$ $\therefore \sin ^{2} x+\operatorname{cosec}^{2} x=9-2=7$ $\therefore \sin ^{4} x+\operatorname{cosec}^{4} x+2 \sin ^{2} x \operatorname{cosec}^{2} x=49$ $\therefore \sin ^{4} x+\operatorname{cosec}^{4} x=49-2=47$

Asked in: MHT CET 2020 (20 Oct Shift 2)

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