Prove that `costheta+cos2theta+cos3theta+…+cosntheta= (sin(ntheta)/2 cos, (n+10/2 theta))/(sin, theta/2)`

Prove that cos^2 theta cosec theta+sin theta=cosec theta

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta

Prove that : (sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

Prove that sin(2theta)/(1-cos2theta)=cot theta

Using induction, prove that cos theta · cos 2theta · cos 2^2 theta. ... cos 2^(n-1) theta =(sin2^n theta)/(2^n sin theta)

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .

Prove that cos theta cos 2 theta cos 4 theta…. Cos 2 ^(n-1) theta = ( sin ( 2 ^(n) theta))/( 2 ^(n) (sin theta)) .

costheta+cos2theta+cos3theta+.......+cos(n-1)theta+cosntheta=

Prove that : cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)