[Brief Comment] Lagrange's trigonometric identity

Lagrange's trigonometric identity

 

$$\begin{array}{r}\sum _{k=0}^n\cos (k\theta )=\frac{1}{2}+\frac{\sin [(2n+1)\theta /2]}{2\sin (\theta /2)},0<\theta <2\pi \end{array}$$

 

다음을 이용하면 쉽게 유도가 가능하다.

$$\begin{array}{r}\sum _{k=0}^n{z}^k=\frac{1-z^{n+1}}{1-z},z\ne 1\end{array}$$