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Advanced Functions/Trig

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Prove the identity:
cos^4 x + sin^4 x = 1 - (1/2)sin^2 (2x)

  • Advanced Functions/Trig -

    LS = cos^4 x + sin^4 x
    = (cos^2 x + sin^2 x)^2 - (2sin^2 x)(cos^2 x)
    = 1 - 2(sin^2 x)(cos^2 x) , now recall sin(2x) = 2sinxcosx
    = 1 - (2sinxcosx)(sinxcosx)
    = 1 - sin(2x) (1/2)sin(2x)
    = 1 - (1/2) sin^2 (x)
    = RS

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