17. Вычислите 3(cos 20°-sin 20°) ------------- √2 sin 25°

Преобразуем выражение:

\(\frac{3(\cos 20^\circ - \sin 20^\circ)}{\sqrt{2} \sin 25^\circ} = \frac{3\sqrt{2}(\frac{1}{\sqrt{2}}\cos 20^\circ - \frac{1}{\sqrt{2}}\sin 20^\circ)}{\sqrt{2} \sin 25^\circ} = \frac{3(\cos 45^\circ \cos 20^\circ - \sin 45^\circ \sin 20^\circ)}{\sin 25^\circ} = \frac{3\cos(45^\circ + 20^\circ)}{\sin 25^\circ} = \frac{3\cos 65^\circ}{\sin 25^\circ}\) \(\because \cos(90^\circ - x) = \sin x\), следовательно, \(\cos 65^\circ = \cos(90^\circ - 25^\circ) = \sin 25^\circ\). Тогда: \(\frac{3\cos 65^\circ}{\sin 25^\circ} = \frac{3\sin 25^\circ}{\sin 25^\circ} = 3\)

Ответ: 3