Goromin D.V.

Is there a value of $x$ such that the equality $\arcsin ^{2} x+\arccos ^{2} x=1$ holds?
According to the inequality between the quadratic mean and the arithmetic mean $\arcsin ^{2} x+\arccos ^{2} x \geq 1 / 2(\arcsin$ $x+\arccos x)^{2}=\pi^{2} / 8>1$.

## Answer

There does not exist.