Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 782

\[ctg\ a = \frac{3}{4}.\]

\[\frac{\sin a \bullet \cos a\ }{\sin^{2}a - \cos^{2}a} = \frac{\frac{\sin a}{\sin^{2}a} \bullet \cos a\ }{\frac{\sin^{2}a}{\sin^{2}a} - \frac{\cos^{2}a}{\sin^{2}a}} =\]

\[= \frac{\frac{\cos a}{\sin a}}{1 - \frac{\cos^{2}a}{\sin^{2}a}} = \frac{\text{ctg\ a}}{1 - ctg^{2}\text{\ a}} =\]

\[= \frac{\frac{3}{4}}{1 - \left( \frac{3}{4} \right)^{2}} = \frac{\frac{3}{4}}{\frac{16}{16} - \frac{9}{16}} =\]

\[= \frac{3}{4}\ :\frac{7}{16} = \frac{3}{4} \bullet \frac{16}{7} = \frac{3 \bullet 4}{7} =\]

\[= \frac{12}{7} = 1\frac{5}{7}.\]