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Math Help - ? Each time you see (cos(2x))^2, replace it with 1/2 + 1/2cos(4x) ?

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    ? Each time you see (cos(2x))^2, replace it with 1/2 + 1/2cos(4x) ?

    I understand sin(2x)^2 = 1/2 - 1/2cos(2x), due to the double number identity: cos2x = 1 - 2sin(x)^2.

    ***[My question is how does (cos(2x))^2 = 1/2 + 1/2cos(4x) ???]***

    I've tried reworking the identity every which way and can't seem to find out how the two are equivalent. Thanks in advance!
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    Quote Originally Posted by estex198 View Post
    I understand sin(2x)^2 = 1/2 - 1/2cos(2x), due to the double number identity: cos2x = 1 - 2sin(x)^2.

    ***[My question is how does (cos(2x))^2 = 1/2 + 1/2cos(4x) ???]***

    I've tried reworking the identity every which way and can't seem to find out how the two are equivalent. Thanks in advance!
    Every which way ....? What about this way:

    \cos (2A) = \cos^2 A - \sin^2 A = 2 \cos^2 A - 1 \Rightarrow \cos^2 A = \frac{1}{2} (\cos (2A) + 1).

    A = 2x in your case.
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    mr fantastic, you made perfect sense of it. Thanks a million. Now I just need to figure out how to get my hair back in my head. Thanks again!

    - Rusty
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