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Question

Prove that (tanθ+1cosθ)2+(tanθ1cosθ)2=2(1+sin2θ1sin2θ)

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Solution

Formula : (a+b)2+(ab)2=2(a2+b2)

LHS is in the form of the above formula

LHS=(tanθ+1cosθ)2+(tanθ1cosθ)2

=2(tan2θ+1cos2θ)

=2(sin2θcos2θ+1cos2θ)

=2(sin2θ+1cos2θ)

=2(1+sin2θ1sin2θ)

=RHS

Hence proved

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