Сравните (sin67°*cos73°+sin73°*cos67°)/(cos55°*cos65°-sin55°*sin65°) и (sin36°+cos36°)/(1-cos72°+sin72°).

\[= \frac{\sin(67{^\circ} + 73{^\circ})}{\cos(55{^\circ} + 65{^\circ})\ } =\]

\[= \frac{\sin{140{^\circ}}}{\cos{120{^\circ}}} < 0;\]

\[так\ как\ \sin{140{^\circ}} > 0;\]

\[\cos{120{^\circ}} < 0.\ \]

\[B = \frac{\sin{36{^\circ}} + \cos{36{^\circ}}}{1 - \cos{72{^\circ}} + \sin{72{^\circ}}} > 0;\ \ \]

\[так\ как\ \sin{36{^\circ}}\ и\ \]

\[\cos{36{^\circ}} > 0 \Longrightarrow\]

\[\Longrightarrow \sin{36{^\circ}} + \cos{36{^\circ}} > 0\ \ \]

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

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

\[\Longrightarrow 1 - \cos{72{^\circ}} + \sin{72{^\circ}} > 0.\]

\[A < B.\]