Prove the following identity :
`sin theta cot theta+ sin theta cosec theta=1 + cos theta`.

Prove the following identity : (sin theta+ cos theta) (sec theta+ cosec theta) =2+ sec theta cosec theta .

Prove the following identity : (tan theta-cot theta)/ (sin theta cos theta)= sec^2 theta- cosec^2 theta .

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

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

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

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

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

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

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

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