Prove that (cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)

Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.

Sum

L.H.S. = `cos θ/(1 - sin θ)`

= `(cos θ(1 + sin θ))/((1 - sin θ)(1 + sin θ))`

= `(cos θ(1 + sin θ))/(1 - sin^2θ)`

= `(cos θ(1 + sin θ))/(cos^2 θ)`

= `( 1 + sin θ)/cos θ`

Hence proved.

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