Prove that `sec theta+tan theta=(cos theta)/(1-sin theta)`

Explanation

Proof: `LHS=sec theta+tan theta`
`=1/(cos theta)+(sin theta)/(cos theta)………[sec theta=1/(cos theta), tan theta=(sin theta)/(cos theta)]`
`=(1+sin theta)/(cos theta)`
`=((1+sin theta))/(cos theta)xx((1-sin theta))/((1- sin theta))`……….. (Multiplying the numerator and denominator by `1-sin theta`)
`=((1)^(2)-sin^(2)theta)/(cos theta(1-sin theta))............[(a+b)(a-b)=a^(2)-b^(2)]`
`=(cos^(2) theta)/(cos theta(1-sin theta)){:[(sin^(2)theta+cos^(2)theta=1),( :.cos^(2)theta=1-sin^(2)theta)]:}`
`=(cos theta)/(1-sin theta)=RHS`
`:. sec theta+tan theta=(cos theta)/(1-sin theta)`