cot^3theta+tan^3theta cot3θ+tan3θ
=cos^3theta/sin^3theta+sin^3theta/cos^3theta=cos3θsin3θ+sin3θcos3θ
=(cos^6theta+sin^6theta)/(sin^3thetacos^3theta)=cos6θ+sin6θsin3θcos3θ
=((cos^2theta+sin^2theta)^3-3(cos^2thetasin^2theta)(cos^2theta+sin^2theta))/(sin^3thetacos^3theta)=(cos2θ+sin2θ)3−3(cos2θsin2θ)(cos2θ+sin2θ)sin3θcos3θ
=(1-3(cos^2thetasin^2theta)*1)/(sin^3thetacos^3theta)=1−3(cos2θsin2θ)⋅1sin3θcos3θ
=(8-24(cos^2thetasin^2theta))/(2^3sin^3thetacos^3theta)=8−24(cos2θsin2θ)23sin3θcos3θ
=(8-6(2costhetasintheta)^2)/(2sinthetacostheta)^3=8−6(2cosθsinθ)2(2sinθcosθ)3
=(8-3*2sin^2 2theta)/(sin^3 2theta)=8−3⋅2sin22θsin32θ
=(8-3*(1-cos4theta))/(1/4(3sin2theta-sin6theta)=8−3⋅(1−cos4θ)14(3sin2θ−sin6θ)
=(5+3cos4theta)/(1/4(3sin2theta-sin6theta)=5+3cos4θ14(3sin2θ−sin6θ)
=(20+12cos4theta)/(3sin2theta-sin6theta)=20+12cos4θ3sin2θ−sin6θ