A polygon of sides

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

A polygon of

n

sides, inscribed in a circle, has sides that subtend angles

2\alpha,4\alpha,\dots,2n\alpha

at the centre of the circle. Prove that its area

A_1

is to the area

A_2

of the regular polygon of

n

sides inscribed in the same circle as

\sin n\alpha:n\sin\alpha