Find the Taylor polynomial of degree $3$ of $f(x)=\cos(x)-\sin(x)$, centered at $x_0=0$

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I'm trying to find the Taylor polynomial of degree $3$ of $f(x)=\cos(x)-\sin(x)$, centered at $x_0=0$. My answer is in the picture below. Are these steps correct?

Procedure

Thanks.