Let t be a real number such that sin(t)/(2)!=0 and let n be a positive integer. Show that the sum from k=1 to n of sinkt is equal to (cos(t)/(2)-cos(n+(1)/(2))t)/(2sin(t)/(2)).

Hence, for each a>0, evaluate the integral.

A) Option A
B) Option B
C) Option C
D) Option D