`(cot theta)/((cosec theta+1))+((cosec theta+1))/(cot theta)=2sec theta`

Prove each of the following identities : (i) (tan theta)/((sec theta -1)) + (tan theta)/((sec theta +1)) = 2 "cosec" theta (ii) (cot theta)/(("cosec" theta +1))+ (("cosec" theta +1))/(cot theta ) = 2 sec theta

prove that tan theta/(sec theta+1)+cot theta/(cosec theta+1)=cosec theta+sec theta-cosec theta. sec theta

(sin theta)/(cot theta+cosec theta)=2+(sin theta)/(cot theta-cosec theta)

Prove that (sin theta)/((cot theta+cosec theta))-(sin theta)/((cot theta-cosec theta))=2

(1)/(cosec theta+cot theta)=cosec theta-cot theta

(tan theta)/(sec theta+1)+(cot theta)/(csc theta+1)=csc theta+sec theta-csc theta sec theta

(1/(cos theta)-1/(sin theta))+1/(cosec theta-cot theta)-1/(sec theta+tan theta) =?

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

The value of (1+cot theta-cosec theta)(1+cos theta+sin theta)sec theta =?

Prove that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)