Question

Prove that: `(sin A - tan A)/(sin A + tan A) = (1 - sec A)/(1 + sec A)`

Answer 1

L.H.S. = `(sin A/sin A - tan A/sin A)/(sin A/sin A + tan A/sin A)`

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

= `(1 - 1/cos A)/(1 + 1/(cos A)`

= `(1 - sec A)/(1 + sec A)` = R.H.S.