Rewrite sin^25xcos^25x simplified using power reduced formulas

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Rewrite sin^25xcos^25x simplified using power reduced formulas

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Ngọc Hoa 3 years 2021-09-03T03:06:54+00:00 1 Answers 8 views 0

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  1. vankhanh
    0
    2021-09-03T03:08:16+00:00
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    Step-by-step explanation:

    The power reducing formulas are given by the following:

    \sin^2 x = \dfrac{1- \cos2x}{2}

    \cos^2 x = \dfrac{1+ \cos2x}{2}

    We can then write the given expression as

    \sin^25x \cos^25x

    = \left(\dfrac{1- \cos 2(5x)}{2} \right) \left(\dfrac{1+ \cos 2(5x)}{2} \right)

    = \dfrac{1}{4}(1- \cos 10x)(1+ \cos 10x)

    = \dfrac{1}{4}(1- \cos^2 10x)

    = \dfrac{1}{4} \left(\dfrac{1- \cos 20x}{2} \right)

    or

    \sin^25x \cos^25x= \dfrac{1}{8}(1- \cos 20x)

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