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Question

If secθ+tanθ=h, then h21h2+1=sinθ.

A
True
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B
False
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Solution

The correct option is A True
h21h2+1=(secθ+tanθ)21(secθ+tanθ)2+1
=sec2θ+tan2θ+2secθtanθ1sec2θ+tan2θ+2secθtanθ+1
=sec2θ1+tan2θ+2secθtanθsec2θ+1+tan2θ+2secθtanθ
=tan2θ+tan2θ+2secθtanθsec2θ+sec2θ+2secθtanθ
=2tan2θ+2secθtanθ2sec2θ+2secθtanθ
=tan2θ+secθtanθsec2θ+secθtanθ
=tanθ(tanθ+secθ)secθ(tanθ+secθ)
=tanθsecθ
=sinθcosθ×cosθ=sinθ

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