How to simpify $\cos x - \sin x$ How does one simplify 

$$\cos x - \sin x$$ 

I tried multiplying by $\cos x + \sin x$, but that just gets me $$\cos x - \sin x = \frac{\cos 2x}{\cos x + \sin x}$$ which is worse. 
Yet wolframalpha gives me $\cos x - \sin x = \sqrt{2}\sin\left(\dfrac{\pi}{4}-x\right)$. How does one obtain this algebraically? 

The reason that it seems like it's hard to simplify this is because it is already in arguably the most simple form. 
cosx-sin is just what it is
if this was cosx-tanx you could do something like this:
cosx- ((sinx)/(cosx))
(((cosx)^2)/(cosx))-((sinx)/(cosx))
(((cosx)^2)-sinx)/(cosx)
but with what you have, you cannot do something like this. 
