If α is the angle which each side of a regular polygon of n sides subtends at its centre, then 1 + cos α + cos 2 α + cos 3 α + … + cos ( n − 1 ) α is equal to

Question

TestHub · Accepted Answer

cos α + cos ( α + β ) + … + cos ( α + ( n − 1 ) β ) = s i n 2 β ​ s i n 2 n β ​ ​ cos ( α + 2 ( n − 1 ) β ​ ) . With first term 1 and common angle α = n 2 π ​ , sin 2 n α ​ = sin π = 0 , so the sum is 0 .

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Options:

Doubts & Discussion