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Math Help - trig identities

  1. #1
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    trig identities

    I'm not sure how to deal with exponent 3 and 4

    1. cos3x = 4cos^3x-3cosx

    2. cos^4 x =1/8(cos4x + 4cos2x + 3)
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) \cos 3x=\cos(x+2x)=\cos x\cos 2x-\sin x\sin 2x

    and use \cos 2x=2\cos^2x-1, \ \sin 2x=2\sin x\cos x, \ \sin^2x=1-\cos^2x

    2) \cos^4x=(\cos^2x)^2

    and use two times the identity \cos^2\alpha=\frac{1+\cos 2\alpha}{2}
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