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 that (1+ cot theta + tan theta ) ( sin theta - cos theta) = (sec theta )/(cosec^(2) theta) - (cosec theta)/(sec^(2)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)/((cot theta + "cosec" theta )) - (sin theta)/((cot theta - "cosec" theta))= 2

Prove the following identity : (tan theta-cot theta)/ (sin theta cos theta)= sec^2 theta- cosec^2 theta .

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

( 1 + tan theta + sec theta ) ( 1 + cot theta - cosec theta ) =

Prove the following identity : (sin theta+ cos theta) (sec theta+ cosec theta) =2+ sec theta cosec 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

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