Ruby Briggs

2022-07-15

Write the Maclaurin series for: $6\mathrm{cos}5{x}^{2}$
Find the first five coefficients.

Kitamiliseakekw

Expert

$\mathrm{cos}x=1-\frac{{x}^{2}}{2!}+\frac{{x}^{4}}{4!}-\frac{{x}^{6}}{6!}+\frac{{x}^{8}}{8!}-\dots$
Thus,
$6\mathrm{cos}\left(5{x}^{2}\right)=6\left[1-\frac{\left(5{x}^{2}{\right)}^{2}}{2}+\frac{\left(5{x}^{2}{\right)}^{4}}{24}-\frac{\left(5{x}^{2}{\right)}^{6}}{720}+\frac{\left(5{x}^{2}{\right)}^{8}}{40320}-\dots \right]$

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