Question

Solve:

$f\left(x\right)=\frac{1-2tanx}{1+2tanx}$

Answer 1

Consider the given function:

$f\left(x\right)=\frac{1-2\tan x}{1+2\tan x}$

$=\frac{2(1-\tan x)}{2(1+\tan x)}$

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

$=\frac{1-\frac{\sin x}{\cos x}}{1+\frac{\sin x}{\cos x}}$

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

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

Hence this is the answer.