Prove the following identity :
`(1+ cot A+tan A) (sin A-cos A) =(secA)/(cosec^2 A)- (cosec A)/(sec^2A)`.

Prove the following identity : (1 - tan x)^2+(1 -cot x)^2 = (sec x -cosec x)^2 .

Prove the following : (cot A - cos A)/(cot A + cos A) = (cosec A -1)/(cosec A + 1) .

Prove the following identity : sqrt ((1+cos theta)/ (1-cos theta)) = cosec theta+cot theta

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

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

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

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

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

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

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