Вычислите (1-cosa)(1+cosa)/(2sina), если sina=-2/3.

\[\frac{\left( 1 - \cos\alpha \right)\left( 1 + \cos\alpha \right)}{2\sin\alpha} =\]

\[= \frac{1 - \cos^{2}\alpha}{2\sin\alpha} = \frac{\sin^{2}\alpha}{2\sin\alpha} = \frac{\sin\alpha}{2}\ \]

\[\sin\alpha = - \frac{2}{3}:\]

\[\frac{\sin\alpha}{2} = - \frac{2}{3}\ :2 = - \frac{2}{3 \cdot 2} = - \frac{1}{3}\]