Докажите равенство (4cos25°-3sin65°)/sin115°=1.

\[\frac{4\cos{25{^\circ}} - 3\sin{65{^\circ}}}{\sin{115{^\circ}}} = 1\]

\[\frac{4\cos{25{^\circ}} - 3\sin\left( \frac{\pi}{2} - 25{^\circ} \right)}{\sin\left( \frac{\pi}{2} + 25{^\circ} \right)} = 1\]

\[\frac{4\cos{25{^\circ}} - 3\cos{25{^\circ}}}{\cos{25{^\circ}}} = 1\]

\[\frac{\cos{25{^\circ}}}{\cos{25{^\circ}}} = 1\]

\[1 = 1.\]