Question

arcsin(x)-arccos(x)=pi/6 find the value of x

Answer 1

\[\sin y = x\]\[y = \arcsin x\]\[\cos (\frac{\pi}{2} - y) = x\]\[\frac{\pi}{2} - y = \arccos x\]\[y = \frac{\pi}{2} - \arccos x\]\[\arcsin x = \frac{\pi}{2} - \arccos x\]\[\arcsin x - \arccos x = \frac{\pi}{6}\]\[\frac{\pi}{2} - \arccos x - \arccos x = \frac{\pi}{6}\]\[\arccos x = \frac{\pi}{6}\]\[x = \cos \frac{\pi}{6} = \frac{1}{2}\sqrt{3}\]