Монгол Бодлогын Сан

Заавар:$$(\sin\alpha-\cos\alpha)^2=1-2\sin\alpha\cos\alpha$$ $$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$$

Бодолт:\begin{gather*} \dfrac{1-(\sin 20^\circ-\cos20^\circ)^2}{\cos40^\circ+\sin^220^\circ}=\dfrac{1-(1-2\sin20^{\circ}\cos20^\circ)}{\cos^220^\circ-\sin^2 20^\circ+\sin^2{20^\circ}}\\ =\dfrac{2\sin20^\circ\cos20^\circ}{\cos^220^\circ}=\dfrac{2\sin20^\circ}{\cos20^\circ}=2\tg20^\circ \end{gather*}