JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
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 ....... .
- A \(350\)
- B \(500\)
- C \(400\)
- D \(250\)
Answer & Solution
Correct Answer
(D) \(250\)
Step-by-step Solution
Detailed explanation
\(15 \sin 4 \alpha+10 \cos ^{4} \alpha=6\) \(15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6\left(\sin ^{2} \alpha+\cos ^{2} \alpha\right)^{2}\) \(\left(3 \sin ^{2} \alpha-2 \cos ^{2} \alpha\right)^{2}=0\) \(\tan ^{2} \alpha=\frac{2}{3} \cdot \cot ^{2} \alpha=\frac{3}{2}\)…
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