I am having a hard time to solve this trigonometric system of equations. The equations is as follows:
We are given $$\tan(x+y)=3$$ $$\tan(x-y) = 2$$ and we need to find $$\tan2x$$
I have tried multiple ways of solving it but can't get the answer. I have tried angle addition and subtraction identities for tangent. Then I have also derived this equation $$\tan(x+y)-1=\tan(x-y)$$and tried it but without any success.
Any help will be appreciated!
And sorry if this is a very simple thing. I am just a new guy in the world of trigonometry.