Prove That Sin^6x + Cos^6x = 1 - 3sin^2xcos^2x - Toppr

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathsQuestionProve that sin6x+cos6x=1−3sin2xcos2xOpen in AppSolutionVerified by Toppr

Consider the left hand sideLHS = sin6x+cos6x=(sin2x)3+(cos2x)3=(sin2x+cos2x)3−3sin2xcos2x(sin2x+cos2x)=(1)3−3sin2xcos2x×1=1−3sin2xcos2x=RHSHence proved.

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∫sin6x+cos6xsin2xcos2xdx=

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