Question

How do you simplify $\cos (x+\mathrm{\pi })$?

Answer 1

Solve for the required value

We can evaluate$\cos (\mathrm{\pi }+x)$ using the trigonometric identity

$\cos (A+B)=\cos \left(A\right)\cdot \cos \left(B\right)-\sin \left(A\right)\cdot \sin \left(B\right)$

So we get,

$\cos (\mathrm{\pi }+x)=\cos \pi \cos x–\sin \pi \sin x$

We know that $\cos \pi =-1$ and $\sin \pi =0$

Therefore

$$\begin{gathered} \cos (\mathrm{\pi }+x)=(-1)\cos x–\left(0\right)\sin x \\ \Rightarrow \cos (\mathrm{\pi }+x)=-\cos x+0 \\ \Rightarrow \cos (\mathrm{\pi }+x)=–\cos x \end{gathered}$$,

Hence, the required answer is $\cos (\mathrm{\pi }+x)=–\cos x$