# Tan2x Formula

Sin 2x, Cos 2x, Tan 2x is the trigonometric formulas which are called as double angle formulas because they have double angles in their trigonometric functions. Let’s understand it by practicing it through solved example.

 $Tan 2x =\frac{2tan x}{1-tan^{2}x}$

## Introduction to Tan double angle formula

let’s look at trigonometric formulae also called as the double angle formulae having double angles

Derive Double Angle Formulae for Tan 2 Theta

$Tan 2x =\frac{2tan x}{1-tan^{2}x}$

$tan(a+b) =\frac{ tan a + tan b }{1- tan a. tanb}$

So, for this let a = b , it becomes

$tan(a+a) =\frac{ tan a +tan a }{1- tan a. tana}$

$Tan 2a =\frac{2tan a}{1-tan^{2}a}$

## Practice Example for tan 2 theta:

Question:

Find tan 2 x, if tan x = 5

Solution:

= $Tan 2x =\frac{2tan x}{1-tan^{2}x}$

= $Tan 2x =\frac{2 x 5}{1- 5^{2}}$

=-1024

= -512 (Simplify it)

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