TITLE: prove the following trig identity
QUESTION [5 upvotes]: For any $x \in [0,1]$ show that $$\arcsin(x)+\arccos(x)=\frac{\pi}{2}$$ Please note that this is not a homework problem, this is something I came across that appears to be true.

REPLY [2 votes]: Draw a right triangle.  Let $x$ be the sine of one of the (non-right) angles.  Then it's the cosine of the other.  If you know that the three angles must add up to $180^\circ$ and one of the three is $90^\circ$, then that does it.