Answer
See below.
Work Step by Step
We must verify $\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}$ with $A=90,B=30$, plugging in these we get: $\cos 90-\cos 30=-2\sin\frac{90+30}{2}\sin\frac{90-30}{2}\\0-\sqrt3/2=-2\sin60\sin(30)\\-\sqrt3/2=-2(\sqrt3/2)(0.5)$
This is true, hence we verified what we had to.