Solve `sin2theta+costheta=0`

Given that tantheta=a/b find sin2theta and cos2theta

Solve costheta+cos3theta-2cos2theta=0 .

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

Show that [[1 , -tan theta ],[ tan theta, 1]][[1, tan theta],[ -tan theta, 1]]^(-1)=[[cos 2 theta, -sin 2 theta],[ sin 2 theta, cos 2 theta]]

Prove that (sin2theta)/(1+cos2theta)=tantheta

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

Solve tan 5theta=cot2theta .

We express ((cos 2theta -i sin 2theta)^(4) (cos 4theta + i sin 4 theta)^(-5))/((cos 3theta + i sin 3theta)^(-2) (cos 3theta -i sin 3theta)^(-9)) in the form of x+iy , we get

solve the equation tan^2theta +cot^2theta=2