Does this formula for a sum of cosines has a name?

Question

On this thread, Bernard kindly gave me the formula

$$\sum_{k=0}^R \cos k \theta = \frac{\sin \frac{(R+1)\theta}{2}}{\sin \frac{\theta}{2}} \cos \frac{R \theta}{2}$$

He describes the formula as well-known. Does it have a name, so I can find a few pages relating to it?

There is no $k$ in your summation. Anyway add the series with $i\sin(k\theta)$ and then it is a geometric series $(e^{i\theta})^k$ — zwim, Apr 21 '18 at 09:15
I know no name. I simply learnt it when I was in last grade of high school. — Bernard, Apr 21 '18 at 09:18
https://math.stackexchange.com/questions/17966/how-can-we-sum-up-sin-and-cos-series-when-the-angles-are-in-arithmetic-pro — lab bhattacharjee, Apr 21 '18 at 09:44

score 1 · Accepted Answer · answered Apr 21 '18 at 09:25

1

Lagrange Trigonometric Identity. See here

answered Apr 21 '18 at 09:25

Thank you. That link says Lagrange's identity is only valid for $0 \lt \theta \lt 2 \pi$. Is this true? I'm after a universal statement - or at least true for all real numbers. – Richard Burke-Ward Apr 21 '18 at 09:34
it is true. If $\theta \notin [0,2\pi ]$ that is not a problem since $\cos \left( k\theta \right)=\cos \left( k\theta +2n\pi \right)$ and you can choose $n$ such that $k\theta +2n\pi \in [0,2\pi ]$. – Apr 21 '18 at 11:11

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