Question

ctg(2п-3 arcsin √ 3/2)

Answer 1

$ctg(3 alpha )=frac{ctg^2 alpha -3ctg alpha }{3ctg^2 alpha -1}\\ctg(2pi -3arcsinfrac{sqrt3}{2})=-ctg(3cdot frac{ pi }{3})=-frac{ctg^2frac{pi }{3}-3ctgfrac{pi }{3}}{3ctg^2frac{pi }{3}-1}=\\=-frac{frac{1}{3}-3cdot frac{sqrt3}{3} }{3cdot frac{1}{3}-1}=-frac{1-3sqrt3}{3cdot (1-1)}; to ; infty$