# How to you simplify cotx + tanx?

We have to evaluate cot x + tan x

### Solution

We know that cot x and tan x can be expressed in terms of sin and cos.

$\cot x=\frac{cos x}{sin x}$ $\tan x=\frac{sin x}{cos x}$ $\cot x +\tan x=\frac{cos x}{sin x} + \frac{sin x}{cos x}$

=$\frac{\cos ^{2}x +\sin ^{2}x}{\cos x.\sin x}$

We know the trigonometric identity ${\cos ^{2}x +\sin ^{2}x}=1$

On substituting in above equation we get

=$\frac{1}{sinx .cos x}$

We know that $\sin 2x=2\sin x\cos x$

=$\sin x\cos x=\frac{sin2x}{2}$

On substituting above value in sin x cos x we get

$\frac{2}{sin 2x}$

We know that 1 /sin x = cosec x

$\frac{2}{sin 2x}$=$2\csc (2x)$

cot x + tan x= $2\csc (2x)$