2 Arctan x=Arccos 1/2

My teacher said to use the 1/2 angle formula, but I don't know how to use it :eek:

2tan^{-1}(x)=cos^{-1}(\frac{1}{2})

2tan^{-1}(x)=\frac{\pi}{3}

tan^{-1}(x)=\frac{\pi}{6}

x=tan(\frac{\pi}{6})

If the question was meant to be a proof, and the angle was x/2 for the arccos function, would that be a valid identity?