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 `

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

Prove each of the following identities : (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta

( 1 + cos theta) ( 1 - cos theta ) cosec^2 theta =

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

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

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

Prove the following identities: (1-cos theta)/(1+cos theta)=(cos ec theta-cot theta)^(2)

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 : (i) sqrt((1+ sin theta)/(1- sin theta)) = ( sec theta + tan theta) (ii) sqrt((1- cos theta)/(1+ cos theta))= ("cosec" theta - cot theta) (iii) sqrt((1+ cos theta)/(1- cos theta))+ sqrt((1- cos theta)/(1+ cos theta)) = 2 "cosec" theta