Монгол Бодлогын Сан

Заавар:$$\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta$$ $$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta$$ ба тухайн тохиолдолд $\alpha=\beta$ бол $$\sin2\alpha=2\sin\alpha\cos\alpha$$ байдаг.

Бодолт:$$\dfrac{\sin75^\circ}{\sin15^\circ}-\dfrac{\cos75^\circ}{\cos15^\circ}=\dfrac{\sin75^\circ\cos15^\circ-\cos75^\circ\sin15^\circ}{\sin15^\circ\cos15^\circ}=$$ $$=\dfrac{\sin(75^\circ-15^\circ)}{\frac12\cdot(2\sin15^\circ\cos15^\circ)}=\dfrac{2\sin 60^\circ}{\sin30^\circ}=\dfrac{2\cdot\frac{\sqrt3}{2}}{\frac12}=2\sqrt3$$