Prove that:
`sqrt((1-sintheta)/(1+sintheta))=sectheta -tan theta`.

Explanation

LHS = `sqrt((1-sintheta)/(1+sintheta))`.
= `sqrt(((1-sintheta))/((1+sintheta))xx((1-sintheta))/((1-sintheta)))`
` =sqrt((1-sintheta)^2/(1^2-sin^2theta))`
`sqrt(((1-sintheta)^2)/(cos^2theta))` ....[`(therefore sin^2theta + cos^2theta=1)/(therefore 1-sin^2theta=cos^2theta)`]
`=(1-sintheta)/(costheta)`
=`(1)/(costheta)-(sintheta)/(costheta)`
`=sec theta -tantheta`
...[`sectheta = 1/(costheta), tan theta = (sintheta)/(costheta)`]
=RHS
`therefore` LHS = RHS
`therefore" "sqrt((1-sintheta)/(1+sintheta))=sec theta-tantheta`.