RÓWNANIA TRYGONOMETRYCZNE zadanie 8.83 rozwiąż równania, proszę o pomoc.....Daje najj

a) [latex]|2sin x-sqrt3|=sqrt3\\2sin x-sqrt3=sqrt3qquad vee qquad 2sin x-sqrt3=-sqrt3\\ 2sin x=2sqrt3quad/:2qquadveeqquad 2sin x=0quad/:2\\ sin x=sqrt3qquadqquadqquad veeqquad sin x=0\\ xin phiqquadqquadqquad veeqquad x=0+2kpiquadveequad x=pi +2kpiqquad kin mathbb C\\\x=kpi,qquad kin mathbb C[/latex] b) [latex]|sqrt3 tgfrac x3|=1\\sqrt3 tgfrac x3=1quad/:sqrt3qquadveeqquad sqrt3 tgfrac x3=-1quad/:sqrt3\\ tgfrac x3=frac1{sqrt3}=frac{sqrt3}3qquadqquadveeqquadqquad tgfrac x3=-frac1{sqrt3}=-frac{sqrt3}3\\ frac x3=frac pi6+kpiqquadqquadveeqquadqquad frac x3=frac{5pi}6+kpi\\\ x=frac pi2+3kpiqquadqquadveeqquadqquad x=frac{5pi}2+3kpi,qquad  kinmathbb C[/latex] c) [latex]ctg(|2x|)=1\\ ctg(2x)=1qquadqquadveeqquadqquad ctg(-2x)=1\\ ctg(2x)=1qquadqquadveeqquadqquad -ctg(2x)=1quad/:(1)\\ ctg(2x)=1qquadqquadveeqquadqquad ctg(2x)=-1\\2x=fracpi4+kpi qquadquad veeqquadqquad 2x=frac34pi+kpi,qquad kinmathbb C\\ x=fracpi8+frac k2pi qquadquad veeqquadqquad x=frac38pi+frac k2pi,qquad kinmathbb C[/latex] d) [latex]2cos(|frac x3|)=-1\\2cos(frac x3)=-1qquadqquadveeqquadqquad2cos(-frac x3)=-1\\2cos(frac x3)=-1qquadqquadveeqquadqquad2cos(frac x3)=-1\\2cos(frac x3)=-1qquad/:2\\ cos(frac x3)=-frac12\\ frac x3=frac23pi+2kpiquadveequadfrac x3=frac43pi+2kpi,qquad kinmathbb C\\\ x=2pi+6kpiquadveequad x=4pi+6kpi,qquad kinmathbb C[/latex] e) [latex]sqrt{sin^2frac x2}=frac{sqrt3}2\\|sinfrac x2|=frac{sqrt3}2\\ sinfrac x2=frac{sqrt3}2qquadqquadveeqquadqquad sinfrac x2=-frac{sqrt3}2\\ frac x2=fracpi4+2kpi qquadquad veeqquadqquad frac x2=frac34pi+2kpi,qquad kinmathbb C\\\ x=fracpi2+4kpi qquadquad veeqquadqquad x=frac32pi+4kpi,qquad kinmathbb C[/latex] f) [latex]sqrt{4cos^2x+4cos x+1}=1\\ sqrt{(2cos x+1)^2}=1\\|2cos x+1|=1\\ 2cos x+1=1qquadqquadveeqquadqquad 2cos x+1=-1\\ 2cos x=0quad/:2qquad veeqquadqquad 2cos x=-2quad/:2\\~ cos x=0quadqquadqquad veeqquadqquad cos x=-1\\\ x=fracpi2+2kpiquadveequad x=frac32pi+2kpiqquadveeqquad x=pi+2kpi,quad kinmathbb C[/latex]