$\displaystyle { \tg \alpha \cdot \tg \beta = \frac{\tg\alpha + \tg\beta} {\ctg \alpha + \ctg \beta} }$

$\displaystyle { \tg \left ( \frac{\pi}{2} - \alpha \right ) = \ctg \alpha }$

$\displaystyle \tg \alpha = \frac{1}{\ctg \alpha }$

$\displaystyle { (\frac{\pi}{2} -\frac{\pi}{8}) = (\frac{4\pi}{8} -\frac{\pi}{8}) = \frac{3\pi}{8} }$

$\displaystyle { \tg \frac{3\pi}{8} \cdot\tg \frac{\pi}{8} +1 = \tg \left ( \frac{\pi}{2} - \frac{\pi}{8} \right ) \cdot\tg {\pi \over 8}+1 =\ctg\frac{\pi}{8} \cdot\tg {\pi \over 8} +1 }$

$1+1=2$