Prove that:
`("cosec"theta)/("cosec"theta-1)+("cosec"theta)/("cosec"theta+1)=2sec^(2)theta`

(cosec theta)/(cosec theta-1)+(cosec theta)/(cosec theta+1)=2sec^2theta

(sec^2theta-1)(cosec^2theta-1)

(cos theta)/(cosec theta+1)+(cos theta)/(cosec theta-1)=2tan theta

sec^2theta/(cosec^(2)theta) =

(sec^2theta-1)(cosec^2theta-1)=1

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

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

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