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

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

Prove that (cot^(2)theta)/(cosec theta+1)=cosec theta-1

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

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

prove that (cosec theta + cot theta)/(cosec theta- cot theta) = (cosec theta +cot theta)^2

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

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

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

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