Prove each of the following identities :
`(sin theta)/((cot theta + "cosec" theta )) - (sin theta)/((cot theta - "cosec" theta))= 2 `

Prove that: (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

Prove the following identity : (sin theta)/(cot theta+ cosec theta)=2+ (sin theta)/(cot theta- cosec 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 : (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta

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

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