$\arcsin x- \arccos x= \pi/6$, difficult conclusion I do not understand a conclusion in the following equation.  To understand my problem, please read through the example steps and my questions below.
Solve: 
$\arcsin x - \arccos x = \frac{\pi}{6}$
$\arcsin x = \arccos x  + \frac{\pi}{6}$
Substitute $u$ for $\arccos x$
$\arcsin x = u + \frac{\pi}{6}$
$\sin(u + \frac{\pi}{6})=x$
Use sum identity for $\sin (A + B)$
$\sin(u + \frac{\pi}{6}) = \sin u \cos\frac{\pi}{6}+\cos u\sin\frac{\pi}{6}$
$\sin u \cos \frac{\pi}{6} + \cos u\sin\frac{\pi}{6} =x$
I understand the problem up to this point.  The following conclusion I do not understand:
$\sin u=\pm\sqrt{(1 - x^2)}$
How does this example come to this conclusion?  What identities may have been used?  I have pondered this equation for a while and I'm still flummoxed.  All advice is greatly appreciated.
Note: This was a textbook example problem

Hint:
if $u=\arccos (x)$ than 
$\cos u=x$ 
and 
$\sin u=\pm\sqrt{1-\cos^2u}=\pm \sqrt{1-x^2}$
substitute and square your equation and you have
$
\frac{3}{4}(1-x^2)=\frac{1}{4}x^2
$
that can be solved, (with care to improper solutions).
