Answer
$x= \dfrac{3 \pi}{4}, \dfrac{ 7 \pi}{4}$
Work Step by Step
Use formula: $\sin (x+y)= \sin x \cos y+\cos x \sin y\\ \cos (x+y)= \cos x \cos y- \sin x \sin y$
Here, we have
$\cos x \cos \pi -\sin x \sin \pi +\sin x \cos \pi +\cos x \sin \pi=0$
This gives: $-\cos x- \sin x=0$
or, $\tan x=-1$
Hence, the solution for $x$ is: $x= \dfrac{3 \pi}{4}, \dfrac{ 7 \pi}{4}$
