[tex]arccos(x) - arcsin(x) = \dfrac{\pi}{6} \\ \\ arccos(x)+arcsin(x)=\dfrac{\pi}{2}\quad (identitate) \\ -------------- \\ 2\cdot arccos(x) \quad \backslash \quad $ $ $ $ $ $ \quad = \dfrac{\pi}{6}+ \dfrac{\pi}{2} \\ \\ \Rightattow 2\cdot arccos(x) = \dfrac{4\pi}{6} \Rightarrow 2\cdot arccos(x) = \dfrac{2\pi}{3} \Rightarrow arccos(x) = \dfrac{\pi}{3} \Rightarrow \\ \\ \Rightarrow \boxed{x = \dfrac{1}{2}}[/tex]
