Сравните (sin56°*cos79°+sin79°*cos56°)/(cos66°*cos44°-sin66°*sin44°) и (sin37°+cos37°)/(1-cos74°+sin74°).

\[= \frac{\sin(56{^\circ} + 79{^\circ})}{\cos(66{^\circ} + 44{^\circ})\ } =\]

\[= \frac{\sin{135{^\circ}}}{\cos{110{^\circ}}} < 0;\ \]

\[так\ как\ \sin{135{^\circ}} > 0;\ \ \ \]

\[\cos{110{^\circ}} < 0.\]

\[B = \frac{\sin{37{^\circ}} + \cos{37{^\circ}}}{1 - \cos{74{^\circ}} + \sin{74{^\circ}}} > 0;\ \ \]

\[так\ как\ \ \sin{37{^\circ}}\ \]

\[и\ \cos{37{^\circ}} > 0 \Longrightarrow\]

\[\Longrightarrow \sin{37{^\circ}} + \cos{37{^\circ}} > 0\ \]

\[для\ 45{^\circ} < a < 90{^\circ};\ \]

\[\sin a > \cos a \Longrightarrow\]

\[\Longrightarrow 1 - \cos{74{^\circ}} + \sin{74{^\circ}} > 0.\]

\[A < B.\]