Trigonometric Ratios and Identities
Equations
JEE Main 2021
Grade 11
Question:
If $15 \sin^4 \alpha + 10 \cos^4 \alpha = 6$ for some $\alpha \in \mathbb{R}$, find the value of $27 \sec^6 \alpha + 8 \csc^6 \alpha$.
Step-by-Step Solution
Key Concept: Let $\sin^2 \alpha = t$. Write the equation as a quadratic in $t$ and solve. Find $\sin^2 \alpha$ and $\cos^2 \alpha$, then compute $\sec^6 \alpha$ and $\csc^6 \alpha$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 250