Упростите выражение:

Решите задачу:

$\frac{1+tg\left(\frac\pi4-\alpha\right)}{1-tg\left(\frac\pi4-\alpha\right)}\\tg\left(\frac\pi4-\alpha\right)=\frac{tg\frac\pi4-tg\alpha}{1+tg\frac\pi4tg\alpha}=\frac{1-tg\alpha}{1+tg\alpha}=\frac{1-\frac{\sin\alpha}{\cos\alpha}}{1+\frac{\sin\alpha}{\cos\alpha}}=\frac{\frac{\cos\alpha-\sin\alpha}{\cos\alpha}}{\frac{\cos\alpha+\sin\alpha}{\cos\alpha}}=\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha}$

$\frac{1+tg\left(\frac\pi4-\alpha\right)}{1-tg\left(\frac\pi4-\alpha\right)}=\frac{1+\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha}}{1-\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha}}=\frac{\frac{\cos\alpha+\sin\alpha+\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha}}{\frac{\cos\alpha+\sin\alpha-\cos\alpha+\sin\alpha}{\cos\alpha+\sin\alpha}}=\frac{2\cos\alpha}{2\sin\alpha}=2ctg\alpha$