Вычислите 4√5 tg(arccos2/3)

Решите задачу:

$4\sqrt5\, tg(arccos \frac{2}{3} )=?\\\\ \alpha =arccos \frac{2}{3}\; \; \; \Rightarrow \; \; \; cos \alpha =\frac{2}{3}\\\\1+tg^2 \alpha =\frac{1}{cos^2\alpha }\quad \Rightarrow \quad tg^2 \alpha = \frac{1}{cos^2 \alpha } -1\\\\tg^2 \alpha = \frac{1}{(\frac{2}{3})^2} -1= \frac{9}{4} -1= \frac{5}{4} \\\\tg \alpha =\pm \sqrt{ \frac{5}{4} }=\pm \frac{\sqrt5}{2} \\\\tg(arccos \frac{2}{3} )=\pm \frac{\sqrt5}{2}$

$4\sqrt5\, tg(arccos \frac{2}{3})=\pm \, 4\sqrt5\cdot \frac{\sqrt5}{2} =\pm \frac{4\cdot 5}{2} =\pm 10$