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Question

If secθ=p2+q2q, then the value of psinθqcosθpsinθ+qcosθ

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Solution

Given secθ=p2+q2q.
We know that,
sec2θ=tan2θ+1
tan2θ+1=p2+q2q2
tan2θ=p2q2
tanθ=pq,pq
psinθqcosθpsinθ+qcosθ=ptanθqptanθ+q=p2qqp2q+qorp2qqp2q+q
=p2q2p2+q2orp2+q2p2q2

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