For-n-N-prove-by-mathematical-induction-that-cos-cos-cos-n-1-cos-n-1-cos-n-1-2-sin-n-2-sin-n-2-

Question Number 76718 by peter frank last updated on 29/Dec/19

F o r n \in N p r o v e b y m a t h e m a t i c a l

i n d u c t i o n t h a t

\cos α + \cos (α + β) + \cos [α + (n - 1) β] + \dots \cos [α + (n - 1) β] =

\frac{\cos [α + (\frac{n - 1}{2}) β] \sin \frac{n β}{2}}{\sin \frac{n}{2}}