Let p sin 2 α + q cos 2 α = m, q sin 2 β + p cos 2 β = n; p ≠ m, n and q ≠ m, n. What is (\frac{\tan ⁡\alpha}{\tan ⁡\beta}) ^{2} equal to?

Correct Answer is : (m−q)(n−p)(m−p)(n−q)

−\frac{(m−q)(n−q)}{(m−p)(n−p)}

−\frac{(m−q)(n−p)}{(m−p)(n−q)}

\frac{(m−q)(n−q)}{(m−p)(n−p)}

\frac{(m−q)(n−p)}{(m−p)(n−q)}

UPSC CDS II 2025 Mathematics Paper

Question : 41 of 100

Marks: +1, -0

Let p sin² α + q cos² α = m, q sin² β + p cos² β = n; p ≠ m, n and q ≠ m, n.
What is (‌

tan⁡α

tan⁡β

)2 equal to?

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