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Question

Prove that sin6x+cos6x=13sin2xcos2x

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Solution

Consider the left hand side
LHS = sin6x+cos6x
=(sin2x)3+(cos2x)3
=(sin2x+cos2x)33sin2xcos2x(sin2x+cos2x)
=(1)33sin2xcos2x×1
=13sin2xcos2x
=RHS
Hence proved.

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