# Math Help - taylor approximations

1. ## 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

2. Originally Posted by acosta0809
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