2sinx(cosx+1)-√3(cosx+1)=0
(cosx+1)(2sinx-√3)=0
cosx=-1
x=π+2πn,n∈Z
-3π≤π+2πn≤-3π/2
-3≤1+2n≤-3/2
-4≤2n≤-5/2
-2≤n≤-5/4
n=-2⇒x=π-4π=-3π
n=-1⇒x=π-2π=-π
sinx=√3/2
x=π/3+2πk U x=2π/3+2πk-3π≤π/3+2πk≤-3π/2
-18≤2+12k≤-9
-20≤12k≤-11
-20/12≤k≤-11/12
k=-1⇒x=π/3-2π=-5π/3
-3π≤2π/3+2πk≤-3π/2
-18≤4+12k≤-9
-22≤12k≤-13
-22/12≤k≤-13/12
нет решения