Prove that: `2\ costhetacos\ (pi/3+theta)cos(pi/3-theta)=cos3theta`

Prove that: 4\ costhetacos\ (pi/3+theta)cos(pi/3-theta)=cos3theta

The sum of all the solution of the equation costhetacos(pi/3+theta)cos(pi/3-theta)=1/4theta in [0,6pi] (A) 15pi (B) 30pi (C) (100pi)/3 (D) none of these

Prove that 4sinthetasin(pi/3+theta)sin((2pi)/3+theta)=sin3theta

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

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

Prove that: costhetacos(theta/2)-cos3thetacos((9theta)/2)=sin((7theta)/2)\ sin4thetadot

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 costhetacos""(theta)/(2)-cos3 thetacos""(9theta)/(2)=sin7thetasin8theta .

Prove that : (2 cos^(3) theta-cos theta)/(sin theta-2 sin^(3)theta)=cot theta

If theta lies in the first quadrant and costheta=8/(17) , then prove that cos(pi/6+theta)+cos(pi/4-theta)+cos((2pi)/3-theta)=((sqrt(3)-1)/2+1/(sqrt(2)))(23)/(17)