BT$\Leftrightarrow \frac{tan\frac{7\pi}8}{1-\frac{sin^2\frac{\pi}{8}}{cos^2 \frac{\pi}8}}=-\frac{tan\frac{\pi}8}{\frac{cos\frac{\pi}4}{cos^2\frac{\pi}8}}=-\frac12.\frac{sin\frac{\pi}4}{cos\frac{\pi}4}=-\frac12tan\frac{\pi}4=-\frac12$
BT$= \frac{tan\frac{7\pi}8}{1-\frac{sin^2\frac{\pi}{8}}{cos^2 \frac{\pi}8}}=-\frac{tan\frac{\pi}8}{\frac{cos\frac{\pi}4}{cos^2\frac{\pi}8}}=-\frac12.\frac{sin\frac{\pi}4}{cos\frac{\pi}4}=-\frac12tan\frac{\pi}4=-\frac12$