# How do you prove (1+tanx)/(1+cotx)=2?

May 24, 2016

This identity is false!!!

#### Explanation:

Simplifying the left side:

#(1 + sinx/cosx)/(1 + cosx/sinx)

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

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

$\sin \frac{x}{\cos} x$

$\tan x$

Hopefully this helps!

May 24, 2016

Another way to prove this false is as follows.

Since $\frac{\tan x}{\tan x} = 1$ and $\tan x \cot x = \tan x \cdot \frac{1}{\tan x} = 1$:

$\textcolor{b l u e}{\frac{1 + \tan x}{1 + \cot x}} \cdot \frac{\tan x}{\tan x}$

$= \frac{\tan x \left(1 + \tan x\right)}{\tan x + \tan x \cot x}$

$= \frac{\tan x \cancel{\left(1 + \tan x\right)}}{\cancel{1 + \tan x}}$

$= \textcolor{b l u e}{\tan x}$