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Question

Question 6
1+cot2 α1+cosec α=cosec α

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Solution

LHS=1+cot2 α1+cosec α=1+cos2 αsin2 α1+1sin α

[cot θ=cos θsin θ and cosec θ=1sin θ]

=1+cos2 αsin α(1+sin α)=sin α(1+sin α)+cos2 αsin α(1+sin α)

=sin α+(sin2 α+cos2 α)sin α(1+sin α)[sin2 θ+cos2 θ=1]

=(sin α+1)sinα(sin α+1)=1sin α[cosec θ=1sin θ]

=cosec α=RHS

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