Question

(sin111°-2cos159°+cos(-90°))/cos21°

Answer 1

$\frac{\sin 111^{\circ}-2\cos 159^{\circ}+\cos(-90^{\circ})}{\cos21^{\circ}}=\frac{\sin(90^{\circ}+21^{\circ})-2\cos(180^{\circ}-21^{\circ})+\cos90^{\circ}}{\cos21^{\circ}}=\\ \\ =\frac{\cos21^{\circ}-2\cdot(-\cos21^{\circ})+0}{\cos^{\circ}}= \frac{\cos21^{\circ}+2\cos21^{\circ}}{\cos21^{\circ}}=\frac{3\cos21^{\circ}}{\cos21^{\circ}}=3$

Ответ: 3