Question

√3-ctg^2(x)-1/2ctgx=0

Answer 1

$frac{ctg^2x-1}{2ctgx}= (frac{cos^2x-sin^2x}{sin^2x}):frac{2cos x}{sin x}=frac{cos2x}{sin^2x}cdotfrac{sin x}{2cos x}=frac{cos2x}{2sin xcos x}=frac{cos2x}{sin2x}=ctg 2x.$

$ctg2x=sqrt3;\\2x=arcctg(sqrt3)+pi k, kin mathbb Z;\\2x=frac{pi}{6}+pi k, kin mathbb Z\\x=frac{pi}{12}+frac{pi k}{2} , kin mathbb Z$