3. Given the equation $\arccos \frac{4}{5}-\arccos \left(-\frac{4}{5}\right)=\arcsin x$, then
(A) $x=\frac{24}{25}$;
(B) $x=-\frac{24}{25}$;
(C) $x=0$;
(D) such an $x$ does not exist.
3. (D)
$\because \arccos \left(-\frac{4}{5}\right)=\pi-\arccos \frac{4}{5}$,
$\therefore$ the original equation is $2 \arccos \frac{4}{5}-\arcsin x=\pi$.
Also, $\because \arccos x$ is a decreasing function,
$\therefore \quad \arccos \frac{4}{5}<\arccos \frac{\sqrt{2}}{2}=\frac{\pi}{4}$.
Also, $-\arcsin x \leqslant \frac{\pi}{2}$,
$\therefore 2 \arccos \frac{4}{5}-\arcsin x<\pi$,
This inequality indicates that there is no $x$ that satisfies the equation.