Тригонометрично уравление

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[ammornil]

[tex]2sin^{2}(x)cos^{2}(x)+sin^{2}(x)=sin^{2}(x)+cos^{2}(x) \Rightarrow 2sin^{2}(x)cos^{2}(x)-cos^{2}(x)=0 \Rightarrow [cos^{2}(x)][sin^{2}(x)-1]=0[/tex]

[tex]cos^{2}(x)=0[/tex] [tex]\cup[/tex] [tex]2sin^{2}(x)-1=0[/tex]
[tex]cos(x)=0[/tex] [tex]\cup[/tex] [tex]sin^{2}(x)=\frac{1}{2}[/tex]

[tex]x_{1}=\pm\frac{\pi}{2} \pm k\pi[/tex] [tex]\cup[/tex] [tex]sin(x)=\pm\frac{\sqrt{1}}{\sqrt{2}} | .\frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]x_{1}=\pm\frac{\pi}{2} \pm k\pi[/tex] [tex]\cup[/tex] [tex]sin(x)=\pm\frac{\sqrt{2}}{2}[/tex]

[tex]x_{1}=\pm\frac{\pi}{2} \pm k\pi[/tex] [tex]\cup[/tex] [tex]x_{2}=-\frac{\pi}{4}\pm k\pi[/tex] [tex]\cup[/tex] [tex]x_{3}=\frac{\pi}{4}\pm k\pi[/tex]