Simplifying $\tan^{-1}\frac{a\sin{x}+b\cos{x}}{a\cos{x}-b\sin{x}}$ How do I get:
$$\tan^{-1}\left(\frac{b}{a}\right)+x$$
from
$$\tan^{-1}\frac{a\sin{x}+b\cos{x}}{a\cos{x}-b\sin{x}}$$
?
There doesn't seem to be anything left to factor and the only identity use I can think of is the that gives me tangent terms in the equation but that didn't lead me anywhere. Any hint would be appreciated.
(Edit: I was simply stuck on this identity that I encountered in a book on dynamical systems so I figured I'd ask here. Not sure what more details I could provide as it's just a trig problem. I hope it doesn't get deleted since the visual hint provided below and selected as best answer could be helpful to others.)

Geometrical proof : can you prove your identity using  the following figure with the indications herein ?

