Докажите равенство (5cos20°-4sin110°)/cos340°=1.

\[\frac{5\cos{20{^\circ}} - 4\sin{110{^\circ}}}{\cos{340{^\circ}}} = 1\]

\[\frac{5\cos{20{^\circ}} - 4\sin\left( \frac{\pi}{2} + 20{^\circ} \right)}{\cos{(2\pi - 20{^\circ})}} = 1\]

\[\frac{5\cos{20{^\circ}} - 4\cos{20{^\circ}}}{\cos{20{^\circ}}} = 1\]

\[\frac{\cos{20{^\circ}}}{\cos{20{^\circ}}} = 1\]

\[1 = 1.\]