Монгол Бодлогын Сан

Заавар: $$\begin{align*} \cos2\alpha&=2\cos^2\alpha-1\\ \sin2\alpha&=2\sin\alpha\cos\alpha\\ \ctg\alpha&=\tg(90^\circ-\alpha) \end{align*}$$

Бодолт: $$\begin{align*} \dfrac{1-\cos 25^{\circ}+\cos 50^{\circ}}{\sin 50^{\circ}-\sin 25^{\circ}}&{}-\tg 65^{\circ}=\dfrac{1-\cos 25^{\circ}+2\cos^2 25^{\circ}-1}{2\sin25^{\circ}\cos25^\circ-\sin 25^{\circ}}-\tg 65^{\circ}\\ &=\dfrac{\cos25^\circ(2\cos25^\circ-1)}{\sin25^\circ(2\cos25^\circ-1)}-\tg65^\circ\\ &=\ctg25^\circ-\tg65^\circ=\tg65^\circ-\tg65^\circ=0 \end{align*}$$