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

Prove that: 2cos theta cos((pi)/(3)+theta)cos((pi)/(3)-theta)=cos3 theta

If x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3)), prove that xy+yz+zx=0

Prove that 5cos theta+3cos(theta+(pi)/(3))+3 lies between -4 and 10.

Prove that 5cos theta+3cos(theta+(pi)/(3))+3 lies between -4 and 10.

If theta = pi/7 prove that cos theta* cos 2theta * cos 3theta = 1/8

Prove that cos theta* cos 2theta* cos2^(2)theta * cos2^(3)theta x... cos 2^(n-1) theta = 1/2^(n) , when theta = pi/(2^(n)+1) .

Solve for theta,theta in[0,pi],cos theta cos2 theta cos3 theta=(1)/(4)

Prove that (cos(pi+theta)cos(-theta))/(cos(pi-theta)cos((pi)/(2)+theta))=-cot theta

If x*cos theta=y*cos(theta+(2 pi)/(3))=2*cos(theta+(4 pi)/(3)) then evaluate xy+yz+zx