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Question:

Prove the following: cos(π+x)cos(-x)sin(π−x)cos(π/2+x) = cot2x

Solution:

LHS=cos(π+x)cos(−x)sin(π−x)cos(π/2+x)=(−cosx)(cosx)(sinx)(−sinx)=cos²xsin²x=cot²x=RHS
Hence proved.