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Question

ifsecθ+tanθ=h,provethath21h21=sinθ

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Solution

Given,
secθ+tanθ=h
To prove:- h21h2+1=sinθ
Proof:-
secθ+tanθ=h
1cosθ+sinθcosθ=h
1+sinθcosθ=h
Squaring both the sides,
(1+sinθ)2cos2θ=h2
(1+sinθ)2(1sin2θ)=h2
(1+sinθ)2(1sinθ)(1+sinθ)=h2
1+sinθ1sinθ=h2
Now using componendo & dividendo, we get
1+sinθ(1sinθ)1+sinθ+1sinθ=h21h2+1
2sinθ2=h21h2+1
sinθ=h21h2+1


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