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Question

Prove the following identities (1-16)

1+cot x+tan x sin x-cos xsec3 x-cosec3 x=sin2 x cos2 x

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Solution

1+cot x+tan x sin x-cos xsec3 x-cosec3 x=sin2 x cos2 x

LHS=1+cotx+tanxsinx-cosxsec3x-cosec3x =1+cosxsinx+sinxcosxsinx-cosx1cos3x-1sin3x =sinx cosx+cos2x+sin2xsinx-cosxsin2xcos2xsin3x-cos3x =1+sinx cosxsinx-cosxsin2x cos2xsinx-cosxsin2x+cos2x+sinx cosx =sin2x cos2x =RHSHence proved.

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