Prove that :
`(tan theta)/(1 - cot theta) + (cot theta)/(1 - tan theta) = 1 + sec theta cosec theta` .

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + cos theta cosec theta

Prove each of the following identities : (tan theta)/((1-cot theta)) + (cot theta)/((1- tan theta)) = (1+ sec theta "cosec" theta)

(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta*cos ec theta

Prove that (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta+tan theta

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

tan theta+(1)/(tan theta)=sec theta cosec theta

Prove that: cot theta + tan theta = cosec theta sec theta .

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

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

prove that: (1-tan theta)^2+(1-cot theta)^2=(sec theta - cosec theta)^2