Take left hand side = cos A / (cos A – sin A)

First we divide numerator and denominator by cos A:

Than {cos A/ cos A} / {(cos A – sin A) / cos A}

= 1 / [1 – (sin A)/(cos A)]

= 1 / (1 – tan A) = Right hand side

Hence cosA/cosA-sinA = 1/1-tanA

Take left hand side = cos A / (cos A – sin A)

First we divide numerator and denominator by cos A:

Than {cos A/ cos A} / {(cos A – sin A) / cos A}

= 1 / [1 – (sin A)/(cos A)]

= 1 / (1 – tan A) = Right hand side

Hence cosA/cosA-sinA = 1/1-tanA