[latex][latex]\1. \cos^4x-sin^4x=sin4x \(cos^2x+sin^2x)(cos^2x-sin^2x)=2sin2x*cos2x \(cos^2x-sin^2x)-2*2sinx*cosx*(cos^2x-sin^2x)=0 \(cos^2x-sin^2x)-4sinxcosx(cos^2x-sin^2x)=0 \(cos^2x-sin^2x)(1-4sinxcosx)=0 \.[cos^2x-(1-cos^2x)](1-4*frac12sin2x)=0 \2cos^2-1=0 vee 1-2sin2x=0 \cosx=-frac{sqrt2}{2}vee cosx=frac{sqrt2}{2}vee sin2x=frac12 \. \x=-frac34pi+2kpivee x=frac34pi+2kpivee 2x=frac16pi+2kpivee \x=-frac14pi+2kpivee x=frac14pi+2kpiimplies x=frac14pi+frac12kpi vee [/latex] [latex]\x=frac{1}{12}pi+kpivee x=frac{5}{12}pi+kpi, kin C \. \2. \sinx*sin2x=cosx*cos2x \sinx*2sinxcosx=cosx(1-2sin^2x) \2sin^2x*cosx-cosx(1-2sin^2x)=0 \cosx(2sin^2x-1+2sin^2x)=0 \cosx=0 vee 4sin^2x-1=0 \cosx=0vee sinx=frac12vee sinx=-frac12 \x=frac12pi+kpivee x=frac16pi+2kpivee x=frac56pi+2kpivee \x=-frac16pi+2kpivee x=frac76pi+2kpiimplies x=frac{pi}{6}+frac13kpi, kin C[/latex] [latex]\3. \2cosalphageq-sqrt3 \cosalpha=-frac{sqrt3}{2} \m.z. alpha=frac56pi+2kpi, alpha=-frac56pi+2kpi, kin C \. \alphain<-frac56pi+2kpi,frac56pi+2kpi>[/latex] Rysunek i wzory w zalaczniku
