Buktikan bahwa :1 – sin2A / cos2A = 1 – tanA / 1 + tanA

Jawab
 
(1 – sin 2A) /cos 2A = (1 – tan A)/(1+ tan A)
(1 – sin 2A)/(cos 2A) =
= (sin x – cos x)² ./( cos² A – sin² A)
= (sin x  – cos x)(sin x – cos x) / ( cos x -sin x)(cos x + sin x)
= -(cos x – sin x) (sin x – cos x) / (cos x – sin x)(cos x +sin x)
= – (sin x – cos x) / (cos x  + sin x)
= (cos x – sin x)/(cos x  +sin x)
= (cos x/cosx  – sin x/cos x)  / (cos x/cos x  +sin x/cos x)
= (1 – tan x) /(1 + tan x)