Answer
$$\cos(\frac{\pi}{2}+x)=-\sin x$$
The formula is verified to be an identity.
Work Step by Step
$$\cos(\frac{\pi}{2}+x)=-\sin x$$
According to the identity of cosine of a sum, we can analyze the left side as follows: $$\cos(\frac{\pi}{2}+x)$$ $$=\cos\frac{\pi}{2}\cos x-\sin\frac{\pi}{2}\sin x$$ $$=0\times\cos x-1\times\sin x$$ $$=-\sin x$$
Which means the left side is equal with the right side. So the formula is verified to be an identity.
