p sin^2 a + q cos^2 a = m: find tan^2 a

This type of question, asked 2 times: CDS 2 2025, CDS 1 2026. All 2 questions below, oldest first.

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Question 1 (case study, 2 parts)
CDS 2 2025
Let $p\sin^2\alpha + q\cos^2\alpha = m$ , $q\sin^2\beta + p\cos^2\beta = n$ ; $p \ne m, n$ and $q \ne m, n$ .
41 $\left(\dfrac{\tan\alpha}{\tan\beta}\right)^2$
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42 $\alpha$
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Question 2 (case study, 2 parts)
CDS 1 2026
For the next two (02) items that follow : $p\sin^2\alpha + q\cos^2\alpha = m$ and $p\cos^2\beta + q\sin^2\beta = n$
95 $\tan^2\alpha$
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96 $\cot^2\beta$
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