Find the Exact Value cot(arcsin(u))

Draw a triangle in the plane with vertices ${\displaystyle (\sqrt{1^2-u^2},u)}$, ${\displaystyle (\sqrt{1^2-u^2},0)}$, and the origin. Then ${\displaystyle \arcsin \left(u\right)}$ is the angle between the positive x-axis and the ray beginning at the origin and passing through ${\displaystyle (\sqrt{1^2-u^2},u)}$. Therefore, ${\displaystyle \cot \left(\arcsin \left(u\right)\right)}$ is ${\displaystyle \frac{\sqrt{1-u^2}}{u}}$.