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

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

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

Show that if n>2cos^(2)((pi)/(n))+cos^(2)((3 pi)/(n))+cos^(2)((5 pi)/(n))+...nterms=(n)/(2)

2 ^ (n-1) (cos theta-cos ((pi) / (n))) (cos theta-cos ((2 pi) / (n))) ... (cos theta-cos ((n- 1) / (n)) pi)

{:(" " Lt),(n rarroo):} (pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)pi)/(2n))=

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+y)

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

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

If m^(2) cos.(2pi)/(15)cos. (4pi)/(15) cos. (8 pi)/(15) cos. (14pi)/(15)=n^(2) , then find the value of (m^(2)-n^(2))/(n^(2)) .

(1+sin phi+i cos phi)/((1+sin phi-i cos phi)^(n))=cos(n(pi)/(2)-n phi)+i sin(n(pi) /(2)-n phi)