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Question

Prove the following identities (1-16)

1-sin2 x1+cot x-cos2 x1+tan x=sin x cos x

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Solution

1-sin2 x1+cot x-cos2 x1+tan x=sin x cos x


LHS= 1-sin3xsinx+cosx-cos3xsinx+cosx=sinx+cosx-sin3x+cos3xsinx+cosx=sinx+cosx1-sin2x-cos2x+sinx cosxsinx+cosx=1-sin2x-cos2x+sinx cosx=1-1+sinx cosx=sinx cosx

= RHS
Hence proved.

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