I'm having truble calculating right side of this equation

$$\cos1 + \cos 2 + \cdots + \cos n = -\frac{1}{2} + \frac{\sin(n+\frac{1}{2})}{2\sin\frac{1}{2}}$$ for $n = 1$.

I've managed to reach that $$cos1 = -\frac{1}{2} + \frac{\cos^2 1 -\cos1 -\sin^2 1}{2(1-\cos1)}$$

Can i get any tips on how to solve this equation? (If it's even correct at this point).

Thanks.