Вычислите (3cos^2a)/(sina-sin^3a), если sina=3/4.

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

\[= \frac{3\cos^{2}\alpha}{\sin\alpha\left( 1 - \sin^{2}\alpha \right)} =\]

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

\[\sin\alpha = \frac{3}{4}:\]

\[\frac{3}{\sin\alpha} = 3\ :\frac{3}{4} = \frac{3 \cdot 4}{3} = 4.\]