Prove that `sqrt[[1-sintheta]/[1+sintheta]]=sectheta-tantheta`

Explanation

Proof: `LHS=sqrt((1-sin theta)/(1+sin theta))`
`=sqrt(((1-sin theta))/((1+sin theta))xx((1-sin theta))/((1-sin theta)))`
`=sqrt(((1-sin theta)^(2))/(1^(2)-sin^(2)theta))`
`=sqrt(((1-sin theta)^(2))/(cos^(2) theta))`………..`(sin^(2) theta+cos^(2)theta=1)`
`=1-(sin theta)/(cos theta)`
`=1/(cos theta)-(sin theta)/(cos theta)`
`=sec theta-tan theta`.........`[sec theta=1/(cos theta), tan theta=(sin theta)/(cos theta)]`
`=RHS`
`:.sqrt(((1-sin theta))/((1+sin theta)))=sec theta-tan theta`