Answer
$\cos(-x)-\sin(-x)=\cos x+\sin x$
Work Step by Step
$\cos(-x)-\sin(-x)=\cos x+\sin x$
Remember that cosine is an even function, so substitute $\cos(-x)$ with $\cos x$. Also, remember that sine is an odd function, so substitute $\sin(-x)$ with $-\sin x$. After those substitutions, the identity is proved
$\cos x-(-\sin x)=\cos x+\sin x$
$\cos x+\sin x=\cos x+\sin x$
