The title just about sums up my question.
Wolfram|Alpha shows it to be $\frac{2 \cos(x) - \sin(x)}{\sqrt {5}}$, while the (extremely simple) derivation I did by hand gives $-\sin(x - \tan^{-1}(2))$ (which wolfram agrees with).
I'm perfectly willing to accept that the two are equal, but I'd like to know why. What is the property or relationship between $\frac{2 \cos(x) - \sin(x)}{\sqrt {5}}$ and $-\sin(x - \tan^{-1}(2))$ that allows you to convert from one form to another without changing the value of the expression?
I've done some looking, and my initial thoughts are that it's a property of the arc tangent, but I haven't been able to find a solid answer.
Thanks in advance for any responses.