Question

Please help what's the exact value for x?

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

Answer 1

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`