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?

  • $\begingroup$ It is an easy corollary of the Euler's formula. $\endgroup$ – Hanul Jeon Apr 21 '18 at 9:14
  • 1
    $\begingroup$ There is no $k$ in your summation. Anyway add the series with $i\sin(k\theta)$ and then it is a geometric series $(e^{i\theta})^k$ $\endgroup$ – zwim Apr 21 '18 at 9:15
  • $\begingroup$ I know no name. I simply learnt it when I was in last grade of high school. $\endgroup$ – Bernard Apr 21 '18 at 9:18
  • $\begingroup$ math.stackexchange.com/questions/17966/… $\endgroup$ – lab bhattacharjee Apr 21 '18 at 9:44

Lagrange Trigonometric Identity. See here

  • $\begingroup$ 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. $\endgroup$ – Richard Burke-Ward Apr 21 '18 at 9:34
  • $\begingroup$ 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 $k\theta +2n\pi \in [0,2\pi ]$. $\endgroup$ – user547564 Apr 21 '18 at 11:11

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