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Question

If tanθ=ab, Prove that asinθbcosθasinθ+bcosθ=a2b2a2+b2.

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Solution

LHS =asinθbcosθasinθ+bcosθ

(divide by cosθ)

=atanθbatanθ+b

=a×abba×ab+b(tanθ=ab)

=a2b2a2+b2=RHS


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