Use the Maclaurin Series For $f(x)=\sin (4 x)$ To Find the Maclaurin Series For

Multiple Choice

Use the Maclaurin series for $f(x) =\sin (4 x)$ to find the Maclaurin series for $f(x) =\cos (4 x)$ .

A) $4 x-\frac{4^{3} x^{3}}{3 !}+\frac{4^{5} x^{5}}{5 !}-\cdots$
B) $1-\frac{4^{2} x^{2}}{2 !}+\frac{4^{4} x^{4}}{4 !}-\cdots$
C) $x-\frac{4^{2} x^{3}}{3 !}+\frac{4^{4} x^{5}}{5 !}-\cdots$
D) $4 x-\frac{4^{2} x^{2}}{2 !}+\frac{4^{3} x^{3}}{3 !}-\cdots$