Prove each of the following identities :
`(i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) `
`(ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta) `

(1-cos theta)/(sin theta)=(sin theta)/(1+cos theta)

(1-cos theta)/(sin theta)=(sin theta)/(1+cos theta)

(cos theta + sin theta )/( cos theta - sin theta )-(cos theta - sin theta )/( cos theta + sin theta ) =

(1 + sin theta-cos theta) / (1 + sin theta + cos theta)

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

(1 + sin theta-cos theta) / (1 + sin theta + cos theta) =

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin 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 : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

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