Question

Вычислите ctg(arccos 4/5)

Answer 1

$ctg(arccos \frac{4}{5} )= \frac{4}{3}\\\\ \alpha =arccos \frac{4}{5} \; ,\\\\ctg \alpha = \frac{cos \alpha }{sin \alpha }= \frac{cos \alpha }{\sqrt{1-cos^2 \alpha }} }=\frac{cos(arccos \frac{4}{5}) }{\sqrt{1-cos^2(arccos \alpha )}} } =\\\\= \frac{4/5}{\sqrt{1-16/25}} = \frac{4}{5\cdot \sqrt{9/25}}=\frac{4}{5\cdot (3/5)}=\frac{4\cdot 5}{5\cdot 3} = \frac{4}{3}$