The method used to find the Maclaurin polynomial of sin(x), cos(x), and ex requires finding several derivatives of the function. However, you can only take a couple derivatives of tan(x) before it becomes unbearable to calculate.
Is there a relatively easy way to find the Maclaurin polynomial of tan(x)?
I considered using tan(x)=sin(x)/cos(x) somehow, but I couldn't figure out how.
Answer
Long division of series.
x+x33+2x515+…1−x22+x424+…)¯x−x36+x5120+…x−x32+x524+…−−−−−−−−x33−x530+…x33−x56+…−−−−−−2x515+…2x515+…−−−−
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