rozwiąż równanie trygonometryczne, sinx sin2x = cosx cos2x

[latex]sinx sin2x=cosx cos2x\sinxcdot2sinx cosx=cosx(cos^2x-sin^2x)\2sin^2x cosx=cosx^3x-cosx sin^2x\cosx(2sin^2x-cos^2x+sin^2x)=0\cosx(3sin^2x-cos^2x)=0\cosx(3sin^2x-1+sin^2x)=0\cosx(4sin^2x-1)=0\cosx=0 vee 4sin^2x=1\cosx=0 vee sin^2x=frac{1}{4}\cosx=0 vee sinx=frac{1}{2} vee sinx=-frac{1}{2}\x=frac{pi}{2}+kpi vee x=frac{pi}{6}+2kpi vee x=frac{5}{6}pi+2kpi vee x=frac{7}{6}pi+2kpi vee x=frac{11}{6}pi+2kpi[/latex]

sinx sin2x = cosx cos2x sin2x≠0 cos x≠0 tg(x)=ctg(2x) tg x= tg(π/2-2x) x=π/2-2x+kπ 3x=π/2+kπ x=π/6+kπ/3 ∈D   ODP x=π/6+kπ/3   Pozdr   Hans