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Question

How do you prove 1+cot2x=cosec2x?


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Solution

Proof of given relation:

1+cot2x=cosec2x

Here we have LHS=1+cot2x

Therefore,

1+cot2x=sin2xsin2x+cos2xsin2x [cotx=cosxsinx]

=sin2x+cos2xsin2x

=1sin2x [sin2x+cos2x=1]

=cosec2x [cosecx=1sinx]

=RHS

Hence, 1+cot2x=cosec2x is proved.


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