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Question

If sec θ tan θ = m, show that m2-1m2+1=sinθ.

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Solution

m2-1m2+1=secθ+tanθ2-1secθ+tanθ2+1
=sec2θ+tan2θ+2secθtanθ-1sec2θ+tan2θ+2secθtanθ+1

=2tan2θ+2secθtanθ2sec2θ+2secθtanθ [Since, sec2θ-1=tan2θ and tan2θ+1=sec2θ ]

=2tanθtanθ+secθ2secθtanθ+secθ=tanθsecθ=sinθcosθ×cosθ=sinθ
Hence, m2-1m2+1=sinθ

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