For the following exercise use the function $C_4(x)=1-\frac{x^2}{2}+\frac{x^4}{24}$ on $-,.$

Plot $co{s}^2(x)-(C_4(x){)}^2$ on $-,.$

Compare the maximum difference with the square of the Taylor remainder estimate for $cos(x).$

What is the maximum value taken by the function $co{s}^2(x)-(C_4(x){)}^2$ when $x$ is in $-,?$

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Use the estimate of the remainder $|R_4(x)|$ for the function $cos(x)$ with which is $($:$|R_4(x)|=\frac{{}^5}{120}$

I can't seem to figure this last question out! Thank you in advanced!