3cosx+2cos^2(3п/2-x)=0

[latex]3cosx+2cos^2( \frac{3 \pi }{2} -x)=0[/latex] [latex]3cosx+2sin^2(x)=0[/latex] [latex]3cosx+2(1-cos^2x)=0[/latex] [latex]3cosx+2-2cos^2x=0 \\ \\ 2cos^2x-3cosx-2=0 [/latex] cosx=t ; t∈[-1;1] [latex]2t^2-3t-2=0 ; t = -\frac{1}{2} ; 2[/latex] t=2∉[-1;1], значит, t=-1/2 [latex]cosx=- \frac{1}{2} [/latex] x=+/- 2π/3+2πk, k∈Z