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

If theta =(pi)/(2 ^(n) +1), then cos theta cos 2 theta cos 2^(2) theta …cos 2 ^(n-1)theta is equal to

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

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)

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 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)

lim_(n rarr oo)n sin\ (2 pi)/(3n)*cos\ (2 pi)/(3n)

The general solution of the equation 8cos x cos2x cos4x=(sin6x)/(sin x) is x=((n pi)/(7))+((pi)/(21)),AA n in Zx=((2 pi)/(7))+((pi)/(14)),AA n in Zx=((n pi)/(7))+((pi)/(14)),AA n in Zx=(n pi)+((pi)/(14)),AA n in Z

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