# Math Help - Proving identities

1. ## Proving identities

2tanA / 1+tan2A = sin2A

I know that 2tanA is tan a + tan a and that sin2A is 2sinAcosA

Could someone help me figure out the rest?

2. ## Re: Proving identities

Traditionally, when proving identities you want to begin with one side (usually the left) and apply known standard identities and perhaps some algebra so that the right side results. Looking at the left side, I suggest you begin with the Pythagorean identity $1+\tan^2\theta=\sec^2\theta$.

3. ## Re: Proving identities

Hi

$\\\mathrm{\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}}\\\mathrm{\tan(2A)=\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\dfrac{\sin2A}{\cos2A}=\dfrac{2 \tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\cos2A\times\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\dfrac{\cos^2A-\sin^2A}{\cos^2A+\sin^2A}\times\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\dfrac{1-\tan^2A}{1+\tan^2A}\times\dfrac{2\tan A}{1-\tan^2A}}\\\mathrm{\sin2A=\dfrac{2\tan A}{1+\tan^2 A}}$

Greetings