if cosec A-sinA=p and secA-cosA=q, prove that p^2q^2(p^2+q^2+3)=1
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LHS :
q(p2−1)
=(secθ+cosec θ)[(sinθ+cosθ)2−1]
=(cosθ1+sinθ1)(2sinθcosθ)
=(sinθcosθsinθ+cosθ)(2sinθcosθ)
=2(sinθ+cosθ)=2p = RHS
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This is your required proof.
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