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

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

Prove the following identity : cosec^6 theta- cot^6 theta =3 cot^2 theta cosec^2 theta+1 .

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

Prove the following identity : 2 (sin^6 theta+ cos^6 theta)-3 (sin^4 theta+ cos^4 theta)+1=0 .

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

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

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

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