Prove that (1 - sin 2A)/(1 + sin 2A) = (1 - tan A)/(1 + tan A)

Question

This is a proving trigonometric identities question, though there is a  square root involved

Answer 1

Remeber the formula Sin2a  = 2SinaCosa

Sin^2a+Cos^2a = 1

Sina/Cosa = Tana

Given (1-Sin2a)/(1+Sin2a)

Left hand side identity =

= (1-Sin2a)/(1+Sin2a)

= (Cos^2A+Sin^2a-Sin2a)/(Cos^2A+Sin^2a+Sin2a)

= (Cos^2A+Sin^2a-2SinaCosa)/((Cos^2A+Sin^2a+2SinaCosa)

= (Cosa-Sina)^2/(Cosa+Sina)^2

Multiple to numarator and denominator by Cosa.

= (1-Tana)^2/(1+Tana)^2

= [(1-Tana)/(1+tana)]^2

= Right hand side identity.