\[\boxed{\mathbf{1039.}}\]
\[1)\sin a \bullet \cos{2a} + \sin{2a} \bullet \cos a =\]
\[= \sin(a + 2a) = \sin{3a}\]
\[2)\sin{5\beta} \bullet \cos{3\beta} -\]
\[- \sin{3\beta} \bullet \cos{5\beta} =\]
\[= \sin(5\beta - 3\beta) = \sin{2\beta}\]