Монгол Бодлогын Сан

Заавар: $$\tg(\alpha-\beta)=\dfrac{\tg\alpha-\tg\beta}{1+\tg\alpha\cdot\tg\beta}\Rightarrow$$ $$\tg\alpha-\tg\beta=\tg(\alpha-\beta)\cdot(1+\tg\alpha\cdot\tg\beta)$$

Бодолт: $$\cos4\alpha+1=\cos60^\circ+1=\dfrac32$$ $$\ctg\alpha-\tg\alpha=\ctg15^\circ-\tg15^\circ=\tg75^\circ-\tg15^\circ=$$ $$=\tg(75^\circ-15^\circ)\cdot(1+\tg75^\circ\cdot\tg15^\circ)=\tg60^\circ\cdot 2=2\sqrt3$$ тул $$\dfrac{\cos4\alpha+1}{\ctg\alpha-\tg\alpha}=\dfrac{\frac32}{2\sqrt3}=\dfrac{\sqrt3}{4}$$