Вычислите (2sin^2a)/(cosa-cos^3a), если cosa=2/7.

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

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

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

\[\cos\alpha = \frac{2}{7}:\]

\[\frac{2}{\cos\alpha} = 2\ :\frac{2}{7} = \frac{2 \cdot 7}{2} = 7.\]