Монгол Бодлогын Сан

Заавар:

Бодолт: $$\begin{align*} \tg2\alpha+\sec2\alpha&=\dfrac{\sin2\alpha}{\cos2\alpha}+\dfrac{1}{\cos2\alpha}=\dfrac{\sin2\alpha+1}{\cos2\alpha}\\ &=\dfrac{1+\sin2\alpha}{\cos^2\alpha-\sin^2\alpha}=\dfrac{\sin^2\alpha+\cos^2\alpha+2\sin\alpha\cos\alpha}{\cos^2\alpha-\sin^2\alpha}\\ &=\dfrac{(\sin\alpha+\cos\alpha)^2}{(\cos\alpha-\sin\alpha)(\cos\alpha+\sin\alpha)}=\dfrac{\sin\alpha+\cos\alpha}{\cos\alpha-\sin\alpha} \end{align*}$$