Question

$y=\frac{\cos x+\sin x}{\cos x-\sin x};$ write in terms of tan

Answer 1

Given

$y=\frac{\cos x+\sin x}{\cos x-\sin x}$

Dividing numerator and denominator by $cosx$

$y=\frac{1+\tan x}{1-\tan x}$ We know $\tan 45=1$

$=\frac{\tan 45+\tan x}{1-1\times \tan x}=\frac{\tan 45+\tan x}{1-\tan 45\tan x}$

$=\tan (45+x)$