11.23 Compute $\sin \left(\arcsin \frac{3}{5}+\arccos \frac{1}{3}\right)$.
11.23 According to formula (4.7), we find

$$
\begin{aligned}
& \sin \left(\arcsin \frac{3}{5}\right) \cos \left(\arccos \frac{1}{3}\right)+\cos \left(\arcsin \frac{3}{5}\right) \sin \left(\arccos \frac{1}{3}\right)= \\
& =\frac{3}{5} \cdot \frac{1}{3}+\sqrt{1-\frac{9}{25}} \sqrt{1-\frac{1}{9}}=\frac{1}{5}+\frac{4}{5} \cdot \frac{2 \sqrt{2}}{3}=\frac{3+8 \sqrt{2}}{15}
\end{aligned}
$$