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

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

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

Prove that: cos^2(pi/4-theta)-sin^2(pi/4-theta)=sin2theta

Prove that: (a) (sin 2 theta)/(1+cos 2 theta)=tan theta (b) (1+sin 2 theta+cos 2theta)/(1+sin2 theta-cos 2 theta)=cot theta

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

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

Prove that cos^(2)theta("cosec"^(2)theta-cot^(2)theta)=cos^(2)theta .