Question

please help what's the exact value for x?

cos(x+pi)-sin(x-pi)=0
SHOW WORK PLEASE​

Answer 1

Step-by-step explanation:

Recall that

$\cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi$

and

$\sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi$

But we also know that

$\cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \:$

so the above relations reduce to

$\cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x$

Therefore,

$\cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x$