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Math Help - taylor approximations

  1. #1
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    taylor approximations

    the question is

    Find the Taylor series expansion about x = 0 for cos^x using the series for
    2 sin x cos x.

    i found the series for 2 sinx cosx by using the sinx since 2 sinx cosx = sin2x

    which is 2x-\frac{4x^3}{3}+\frac{4x^5}{15}+...

    but now im stuck i dont know how 2 sinx cosx can be related to cos^2x
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by acosta0809 View Post
    the question is

    Find the Taylor series expansion about x = 0 for cos^2 x using the series for
    2 sin x cos x.

    i found the series for 2 sinx cosx by using the sinx since 2 sinx cosx = sin2x

    which is 2x-\frac{4x^3}{3}+\frac{4x^5}{15}+...

    but now im stuck i dont know how 2 sinx cosx can be related to cos^2x
    \cos^2(x)=1-\int_0^x 2 \cos(\zeta) \sin(\zeta)\;d\zeta

    so term by term integration of the series for 2 \sin(x)\cos(x) can be used to find the required series

    CB
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