Тригонометрия.1 пример помогите решить.Заранее спасибо)

Решите задачу:

$\frac{tg^2\frac{5\pi}{24}tg^2\frac{\pi}{24}-1}{tg^2 \frac{5\pi}{24}-tg^2 \frac{\pi}{24}}=\\\\\frac{tg\frac{5\pi}{24}tg\frac{\pi}{24}+1}{tg \frac{5\pi}{24}-tg\frac{\pi}{24}}*\frac{tg\frac{5\pi}{24}tg\frac{\pi}{24}-1}{tg\frac{5\pi}{24}+tg\frac{\pi}{24}}=$
$\frac{1}{tg(\frac{5\pi}{24}+\frac{\pi}{24})}*\frac{1}{tg(\frac{5\pi}{24}-\frac{\pi}{24})}=\\\\$ $\frac{1}{tg \frac{\pi}{4}*tg \frac{\pi}{6}}=\frac{1}{1*\frac{1}{\sqrt{3}}}=\sqrt{3}$