Prove the following identity :
`sec^4 theta- tan^4 theta =1+2 tan^2 theta`.

Prove the following identity : sec^6 theta- tan^6 theta=1+3 tan^2 theta+3 tan^4 theta .

Prove the following identity : 2 sec^2 theta- sec^4 theta-2 cosec^2 theta+ cosec^4 theta= cot^4 theta-tan^4 theta .

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Prove the following identity : sqrt (sec^2 theta+ cosec^2 theta)= tan theta+ cot theta= sec theta cosec theta .

Prove the following identity : 1/(sec theta-tan theta)= (1+sin theta)/(cos theta) = sec theta+tan theta .

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

Prove the following identity : (1+cos theta)/(1-cos theta)= (tan^2 theta)/((sec theta-1)^2) .

Prove the following identity : 1/(sec theta+tan theta)= (1-sin theta)/(cos theta) = sec theta-tan theta .

Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot theta) .