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March 28, 2017

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Verify the identity.

cos 4x + cos 2x = 2 - 2 sin^2(2x) - 2 sin^2 x

  • Trig - ,

    using the identity
    cos 2A = cos^2 A - sin^2 A = 1 - 2sin^2 x = 2cos^2 x -1

    LS = cos 4x + cos 2x
    = cos^2 2x - sin^2 2x + cos 2x
    = (1 - sin^2 (2x) ) - sin^2 (2x) + (1 - 2sin^2 x)
    = 1 - 2sin^2 (2x) + 1 - 2sin^2 x
    = 2 - 2sin^2 (2x) - 2sin^2 x
    = RS

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