Answer
$${\text{False}}$$
Work Step by Step
$$\eqalign{
& {\arcsin ^2}x + {\arccos ^2}x = 1 \cr
& {\text{Let }}x = \frac{{\sqrt 2 }}{2},{\text{ then}} \cr
& {\arcsin ^2}x + {\arccos ^2}x = {\arcsin ^2}\left( {\frac{{\sqrt 2 }}{2}} \right) + {\arccos ^2}\left( {\frac{{\sqrt 2 }}{2}} \right) \cr
& {\arcsin ^2}x + {\arccos ^2}x = {\left( {\frac{\pi }{4}} \right)^2} + {\left( {\frac{\pi }{4}} \right)^2} \cr
& {\arcsin ^2}x + {\arccos ^2}x = \frac{{{\pi ^2}}}{8} \cr
& {\text{Therefore, the statement is false}}{\text{.}} \cr} $$