Ребята! Помогите решить cosx-1=sinx/2

[latex]cosx-1=sin \frac{x}{2} [/latex] [latex]-(1-cosx)=sin \frac{x}{2} [/latex] [latex][sin^2 \frac{x}{2} = \frac{1-cosx}{2}] [/latex] [latex]-2sin^2 \frac{x}{2} -sin \frac{x}{2} =0[/latex] [latex]2sin^2 \frac{x}{2}+sin \frac{x}{2} =0[/latex] [latex]sin \frac{x}{2}(2sin \frac{x}{2}+1) =0[/latex] 1) [latex]sin \frac{x}{2} =0[/latex]  [latex] \frac{x}{2} = \pi k,[/latex] [latex]k[/latex] ∈ [latex]Z[/latex] [latex]x=2 \pi k,[/latex] [latex]k[/latex] ∈ [latex]Z[/latex] 2) [latex]2sin \frac{x}{2}+1 =0[/latex] [latex]2sin \frac{x}{2}=-1[/latex] [latex]sin \frac{x}{2}=- \frac{1}{2} [/latex] [latex] \frac{x}{2} =(-1)^{n+1} \frac{ \pi }{6} + \pi n,[/latex] [latex]n[/latex] ∈ [latex]Z[/latex] [latex]x} =(-1)^{n+1} \frac{ \pi }{3} + 2\pi n,[/latex] [latex]n[/latex] ∈ [latex]Z[/latex]