Answer
See the details below.
Work Step by Step
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 $$(\sin^{-1}x)'=-(\cos^{-1}x)'.$$
