[latex]\(2-cos2x)(2+cos2x)=sinxcdot cosx+ dfrac{7}{2} \ \4-cos^22x= dfrac{1}{2} sin2x+ dfrac{7}{2} \ \-(1-sin^22x)- dfrac{1}{2} sin2x+4- dfrac{7}{2} =0 \ \sin^22x-1- dfrac{1}{2} sin2x+ dfrac{1}{2} =0/cdot2 , sin2x=t \ \2t^2-t-1=0 \ \2t^2+t-2t-1=0 \ \t(2t+1)-(2t+1)=0 \ \(2t+1)(t-1)=0 \ \2t+1=0 vee t-1=0[/latex] [latex]\sin2x=- dfrac{1}{2} vee sin2x=1 \ \2x=- dfrac{ pi} {6} + 2kpi vee 2x= dfrac{7}{6} pi +2kpi vee 2x= frac{ pi} {2} +2kpi /:2 \ \sprowadzamy x do przedzialu extless 0;pi extgreater : \ \x=- frac{1}{12} pi +pi= dfrac{11}{12} pi vee x= dfrac{7}{12} pi vee x= dfrac{ pi} {4} [/latex]
