Question

Ctg(arccos 1+2 arcctg( - корень из 3/2)) ВЫЧИСЛИТЕ!

Answer 1

$ctg(arccos1+2arcctg(-\frac{\sqrt3}{3}))=ctg(0+2(\pi -arcctg\frac{\sqrt3}{3}))=\\\\=ctg(2\pi -2\frac{\pi}{3}))=ctg(-2\cdot \frac{\pi}{3})=-ctg\frac{2\pi}{3}=-ctg(\pi -\frac{\pi}{3})=\\\\=-(-ctg\frac{\pi}{3})=\frac{\sqrt3}{3}$

Answer 2

Ctg(arccos1+2arctg(-√3/3))=ctg(0+2*4π/3)=ctg8π/3=ctg(3π-π/3)=
-ctgπ/3=-√3/3