Prove that `cos^2 theta cosec^2 theta+sin^2 theta=cosec^@ theta`

Prove that cos^2 theta cosec theta+sin theta=cosec theta

Prove that, sin^2 theta+ cosec^2 theta>=2

Prove that, sec^2theta+cosec^2theta=sec^2theta*"cosec"^2theta.

Prove that : (tan theta+cot theta)^2=sec^2 theta+cosec^2 theta=sec^2 theta cosec^2 theta

Prove that cosec^(2) theta + sec^(2) theta = cosec^(2) theta sec^(2) theta .

Prove that (sec^2theta-sin^2theta)/tan^2theta=cosec^2theta-cos^2theta .

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

Prove that (tan^2 theta)/(tan^2 theta-1)+(cosec^2 theta)/ (sec^2 theta-cosec^2 theta)= -sec 2 theta .

Prove that ((1+cot theta +tan theta)(sin theta - cos theta))/(sec ^3 theta -cosec^3 theta) = sin^2 theta cos^2 theta.

Prove that: ((1+cot theta+ tan theta)(sin theta-cos theta))/(sec^3 theta-cosec^3 theta)=sin^2 theta cos^2 theta