If B be the exterior angle of a regular polygon of n sides and A is any constant, then prove that
$sin A + sin (A + B) + sin (A + 2 B) + . . . n$ terms = 0

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Solution

(i) We have $B = \frac{2 π}{n}$
= even multiple of $\frac{π}{n}$ $∴ \frac{n B}{2} = π$
and $s i n \frac{n B}{2} = s i n π = 0$
(ii) Proceed as above.

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