Question

sin^2x - (1+√3)sinx*cosx + √3*cos^2x=0

Answer 1

$sin^2x-(1+sqrt3)sinxcosx+sqrt3 cos^2x=0 |cos^2x, ; cosx neq 0\tg^2x-(1+sqrt 3)tgx+sqrt 3=0\tg^2x-tgx-sqrt 3 tgx+sqrt 3=0\tgx(tgx-1)-sqrt 3(tgx-1)=0\(tgx-1)(tgx-sqrt3)=0\\tgx-1=0\tgx=1\x=frac{pi}{4}+pi n, ; nin Z;\\tgx-sqrt3=0\tgx=sqrt3\x=frac{pi}{3}+pi n, ; nin Z.$