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

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

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

Prove each of the following identities : ((1+ tan^(2) theta) cot theta)/("cosec"^(2) theta ) = tan theta

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

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

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

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

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

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