Step-by-step explanation:
Recall that
[tex] \cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi[/tex]
and
[tex] \sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi[/tex]
But we also know that
[tex] \cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \: [/tex]
so the above relations reduce to
[tex] \cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x [/tex]
Therefore,
[tex] \cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x [/tex]
