tantheta - cot^2thetatanθ−cot2θ
On handiling these kind of problem apply your previous knowledge on identity.
tantheta = sintheta/costhetatanθ=sinθcosθ
cottheta = costheta/sinthetacotθ=cosθsinθ
sin^2theta = 1-cos^2thetasin2θ=1−cos2θ
Our problem:
tantheta - cot^2thetatanθ−cot2θ
=sintheta/costheta - cos^2theta/sin^2theta=sinθcosθ−cos2θsin2θ
=sqrt(1-cos^2theta)/cos(theta) - cos^2theta/(1-cos^2theta)=√1−cos2θcos(θ)−cos2θ1−cos2θ
=(sqrt(1-cos^2theta)(1-cos^2theta))/(costheta(1-cos^2theta)) -(cos^2thetacostheta)/(costheta(1-cos^2theta)=√1−cos2θ(1−cos2θ)cosθ(1−cos2θ)−cos2θcosθcosθ(1−cos2θ)
=((1-cos^2theta)^(3/2)-cos^3theta)/(costheta(1-cos^2theta))=(1−cos2θ)32−cos3θcosθ(1−cos2θ)
