show that `cos2thetacos(theta/2)-cos3thetacos((9theta)/2)=sin5thetasin((5theta)/2)`

cos2 theta*cos(theta/(2))-cos3 theta*cos((9theta)/2)=sin5 theta*sin((5theta)/(2))

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

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

Prove that : sintheta/cos(3theta)+sin(3theta)/cos(9theta)+sin(9theta)/cos(27theta)=1/2(tan(27theta)-tan(theta))

Prove: tan^2thetacos^2theta=1-cos^2theta

The expression (sin8thetacostheta-sin6thetacos3theta)/(cos2thetacostheta-sin3thetasin4theta) is equals-

Let f_n(theta)=(cos(theta/2)+cos2theta+cos((7theta)/2)+....+cos(3n-2)(theta/2))/(sin(theta/2)+sin2theta+sin((7theta)/2)+....+sin(3n-2)(theta/2)) then (a) f_3((3pi)/(16))=sqrt(2)-1 (b) f_5(pi/(28))=sqrt(2)+1 (c) f_7(pi/(60))=(2+sqrt(3)) (d) none of these

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 (cos 3theta+ 2 cos 5theta+ cos 7theta)/( cos theta+ 2 cos 3theta+ cos 5theta)= cos 2theta- sin 2theta tan 3theta .

The expression (sin 8thetacos theta-sin6 thetacos 3 theta)/(cos 2 thetacos theta-sin 3 thetasin 4 theta) is equals:-