University Calculus: Early Transcendentals (3rd Edition)

$$\cos(\pi+x)=-\cos x$$
$$\cos(\pi+x)$$ Apply the addition formula for cosine: $$\cos(\pi+x)=\cos\pi\cos x-\sin\pi\sin x$$ $$\cos(\pi+x)=(-1)\times\cos x-0\times\sin x$$ $$\cos(\pi+x)=-\cos x$$