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)) `

Prove each of the following identities : `(i) (sec theta -1)/(sec thet

1.	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)) `
Answer» (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)).`

`1/(c o s e ctheta-cottheta)-1/(sintheta)=1/(sintheta)-1/(c o s e ctheta+cottheta)`
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