## Calculus (3rd Edition)

Two angles are complementary when they add up to 90 degrees. Thus the geometric interpretation of the identity $$\sin^{-1}x+\cos^{-1}x=\frac{\pi}{2}$$ means that $\sin^{-1}x$ and $\cos^{-1}x$ are complementary. Also, we have $$\sin^{-1}x=\frac{\pi}{2}-\cos^{-1}x$$ and this leads to $$(\sin^{-1}x)'=-(\cos^{-1}x)'.$$