`cos^2theta+cos^2thetacot^2theta=cot^2theta`

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Prove the following identities: 1+3cosec^2thetacot^2theta+cot^6theta=cosec^6theta

Prove the following identity : cot^2 theta- cos^2 theta= cot^2 theta cos^2 theta .

cot^(2)theta-cos^(2)theta=cot^(2)theta*cos^(2)theta

Prove that: cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-cot3theta)

Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta

If sin^2theta=cos^3theta prove that, cot^6theta-cot^2theta=1 .

Prove that cos^(2)theta("cosec"^(2)theta-cot^(2)theta)=cos^(2)theta .

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(2sin theta*cos theta-cos theta)/(1-sin theta+sin^(2)theta-cos^(2)theta)=cot theta

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta