\[\boxed{\mathbf{1316}\mathbf{.}}\]
\[\left( 1 + \cos a \right) \bullet tg\frac{a}{2} = \sin a\]
\[2\cos^{2}\frac{a}{2} \bullet \frac{\sin\frac{a}{2}}{\cos\frac{a}{2}} = \sin a\]
\[2\sin\frac{a}{2} \bullet \cos\frac{a}{2} = \sin a\]
\[\sin a = \sin a.\]
\[Что\ и\ требовалось\ доказать.\]