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Math Help - Trigonometric proof

  1. #1
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    Trigonometric proof

    Prove that cos^2(2x) - sin^2(x) = cos^2(x)(2cos(x) - sqrt(3))(2cos(x) + sqrt(3))
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  2. #2
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    Quote Originally Posted by scorpion007 View Post
    Prove that cos^2(2x) - sin^2(x) = cos^2(x)(2cos(x) - sqrt(3))(2cos(x) + sqrt(3))
    cos^2(2x) - sin^2(x)

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

    = (cos^2(x) - 1 + cos^2(x))^2 - 1 + cos^2(x)

    = (2 cos^2(x) - 1)^2 - 1 + cos^2(x)

    = 4 cos^4(x) - 4 cos^2(x) + 1 - 1 + cos^2(x)

    = 4 cos^4(x) - 3 cos^2(x)

    = cos^2(x)(4 cos^2(x) - 3)

    = cos^2(x)(2cos(x) - sqrt(3))(2cos(x) + sqrt(3))
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  3. #3
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    aha, thanks! i understand it now.
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