`(1+1/(tan^2theta))(1+1/(cot^2theta))=1/(sin^2theta-sin^4theta)`

Prove the following identities: (1+tan^(2)theta)+(1+1/(tan^(2)theta))=1/(sin^(2)theta-sin^(4)theta)

Prove each of the following identities : (1+ tan^(2) theta)(1+ cot^(2) theta)=(1)/((sin^(2) theta- sin^(4) theta))

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

Prove that (1+ tan^4 theta)/(1+ tan^2 theta) = sec ^2 theta-2 sin^2theta

Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=(1-2sin^2thetacos^2theta)/(sintheta\ costheta)

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

If 1/(sin^(2)theta)-1/(cos^(2) theta)-1/(tan^(2)theta)-1/(cot^(2)theta)-1/(sec^(2)theta)-1/(cosec^(2)theta)=-3 then find the value of theta .

Prove the following identity : (cot^2 theta)/((1- cosec theta)^2)= (1+sin theta)/(1-sin theta) .

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

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