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Math Help - Lowering Powers - Simplify in terms of cosine

  1. #1
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    Lowering Powers - Simplify in terms of cosine

    Hello,

    Can someone please show me all the algebraic steps for simplifying cos^4x?

    The problem should be

    cos^4x = ((1+cos2x)/2)((1+cos2x)/2)

    thanks!
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  2. #2
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    \cos^4(x) = (\cos^2(x))^2 = \left(\frac{1+\cos(x)}{2}\right)^2 = \left(\frac{1+\cos(x)}{2}\right) \times \left(\frac{1+\cos(x)}{2}\right)

    Have a look at this.

    Table of Trigonometric Identities
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  3. #3
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    Quote Originally Posted by pickslides View Post
    \cos^4(x) = (\cos^2(x))^2 = \left(\frac{1+\cos(x)}{2}\right)^2 = \left(\frac{1+\cos(x)}{2}\right) \times \left(\frac{1+\cos(x)}{2}\right)

    Have a look at this.

    Table of Trigonometric Identities

    Thanks!

    Although i'm stuck at this part, 1/4(cos^4x+2cos^2x+1)

    what else could I do?
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  4. #4
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    You are expanding something that does not need to be expanded. You will only end up back at the start.
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