Prove that : `(tan^(2)theta)/(1+tan^(2)theta)+(cot^(2)theta)/(1+cot^(2)theta)=1`

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 .

(1-cot^(2)theta)/(tan^(2)theta-1)=cot^(2)theta

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

Prove each of the following identities : (tan^(2) theta)/((1+ tan^(2) theta)) + (cot^(2) theta)/((1+ cot^(2) theta)) =1

Prove that : (1-tan^(2)theta)/(cot^(2)theta-1)=tan^(2)theta

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

If 3cot theta=4 then show that (1-tan^(2)theta)/(1+tan^(2)theta)=(cos^(2)theta-sin^(2)theta)

Prove each of the following identities : (tan theta)/((1+ tan^(2) theta)^(2)) + (cot theta)/((1+ cot^(2) theta)^(2)) = sin theta cos theta