Show that if `n gt 2` `cos^2 (pi/n) + cos^2 ((3pi)/n)+ cos^2((5pi)/n)+ ... n terms =n/2`

Evaluate sin(pi/n)+sin((3pi)/n)+sin((5pi)/n)+........ to n terms.

show that : sin^2 alpha + sin^2(alpha +( 2pi)/n) +sin^2(alpha +( 4pi)/n) + ..... n terms = n/2

Show that: cos\ pi/n +cos\ (2pi)/n +…+cos\ (n-1)/n pi =0

If S=cos^2pi/2+cos^2(2pi)/n+....+cos^2((n-1)pi)/(n), then S equals

Prove that: cos^3theta+cos^3 (theta- (2pi)/n)+cos^3 (theta- (4pi)/n)+… to n terms =0

The value of sin pi/n + sin (3pi)/n+ sin (5pi)/n+... to n terms is equal to

f(n) = cot^2 (pi/n) + cot^2\ (2 pi)/n +...............+ cot^2\ ((n-1) pi)/n, ( n>1, n in N) then lim_(n rarr oo) f(n)/n^2 is equal to (A) 1/2 (B) 1/3 (C) 2/3 (D) 1

Prove that: sin^2(pi/6)+cos^2(pi/3)-t a n^2pi/4=-1/2

If 7theta=(2n+1)pi , where n=0,1,2,3,4,5,6 , then answer the following questions. The equations whose roots are cos. (pi)/(7), cos. (3pi)/(7), cos. (5pi)/(7) is

The value of cos(pi/4)*cos(pi/8)*cos(pi/16)....cos(pi/(2^n)) equals