Докажите равенство (3cos50°-4sin40°)/cos130°=1.

\[\frac{3\cos{50{^\circ}} - 4\sin{40{^\circ}}}{\cos{130{^\circ}}} = 1\]

\[\frac{3\cos{50{^\circ}} - 4\sin\left( \frac{\pi}{2} + 50{^\circ} \right)}{\cos(\pi - 50{^\circ})} = 1\]

\[\frac{3\cos{50{^\circ}} - 4\cos{50{^\circ}}}{- \cos{50{^\circ}}} = 1\]

\[\frac{- \cos{50{^\circ}}}{- \cos{50{^\circ}}} = 1\]

\[1 = 1.\]