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

Explanation

(i) `LHS =(((1)/(costheta)-1))/(((1)/(costheta)+1))=((1-costheta))/((1+cos theta))xx((1+costheta))/((1+cos theta))=((1-cos^(2)theta))/((1+cos theta)^(2))=(sin^(2)theta)/((1+cos theta)^(2)).`
(ii) `LHS =(((1)/(costheta)-(sin theta)/(costheta)))/(((1)/(costheta)+(sin theta)/(costheta)))=((1-sin theta))/((1+sin theta))xx((1+sintheta))/((1+sin theta))=((1-sin^(2)theta))/((1+sin theta)^(2))=(cos^(2)theta)/((1+sin theta)^(2)).`