Answer
$$\sqrt{1-\left(\frac{x-h}{r}\right)^2}$$
Work Step by Step
By definition:
$$
y=\arcsin \left(\frac{x-h}{r}\right)
$$
is a number such that:
$$
\sin y=\frac{x-h}{r}
$$
Then we have that:
$$
\sqrt{1-\sin ^{2} y}=\cos y
$$
and thus:
$$
\cos \left(\arcsin \left(\frac{x-h}{r}\right)\right)=\sqrt{1-\left(\frac{x-h}{r}\right)^{2}}
$$
