Solve `costheta+cos3theta-2cos2theta=0`.

Solve sin2theta+costheta=0

Consider the equation sintheta+sin3theta+sin5theta=0 prove that sin3theta(1+2cos2theta)=0

Prove that cos^2theta=(1+cos2theta)/2

Solve tan 5theta=cot2theta .

If sinx +siny +sinz =0 = cos x +cosy +cosz , then find the value of expression cos(theta-x)+cos(theta-y)+cos(theta-z) .

if cos theta_(1) + cos theta_(2) + cos theta_(3)= sin theta_(1) + sin theta_(2) + sin theta_(3)= 0 , then the value of cos (theta_(1) + theta_(2)) + cos (theta_(2) + theta_(3)) + cos (theta_(3) + theta_(1)) is

(b)Show that (sin theta+sin 3theta+sin 5 theta+sin 7 theta)/(cos theta+cos3theta+cos 5 theta+cos 7 theta)=tan 4 theta .

Prove that (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cottheta

Prove that sin (3theta)/(1+2cos 2theta)=sin theta .

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)