Sine series and cosine series/Beginning/Circle formula/Exercise

Compute

${\left(1-{\frac {1}{2}}X^{2}+{\frac {1}{24}}X^{4}\right)}^{2}+{\left(X-{\frac {1}{6}}X^{3}+{\frac {1}{120}}X^{5}\right)}^{2}.$

Is the result surprising, how can you explain it?

Create a solution