MHT CET · Maths · Trigonometric Ratios & Identities
If \(\sin x+\operatorname{cosec} x=3\), then value of \(\sin ^{4} x+\operatorname{cosec}^{4} x\) is
- A 74
- B 47
- C 07
- D 49
Answer & Solution
Correct Answer
(B) 47
Step-by-step Solution
Detailed explanation
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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