4 уравнения

[milena96]

1) 8cos⁴x - 5cos4x = 3
2) 7cos[tex]\frac{x}{4}[/tex] - 4sin[tex]\frac{x}{2}[/tex] = 4cos³[tex]\frac{x}{4}[/tex]
3) sin⁴x + cos⁴x = sin2x - 0,5
4) cos² (x - [tex]\frac{\pi}{8}[/tex] ) - cos² (x + [tex]\frac{\pi}{8}[/tex]) = [tex]\frac{1}{2}[/tex]

[math10.com]

1.[tex]8cos^4 x-5 cos 4x=3[/tex]
[tex]8cos^4 x-5 (2cos^2 2x-1)-3=0[/tex]
[tex]8cos^4 x-10(2cos^4 x -1)+2=0[/tex]
[tex]-12cos^4 x+12=0[/tex]
[tex]cos^4 x-1=0[/tex]
[tex](cos x-1)(cosx+1)(cos^2x+1)=0[/tex]

2.[tex]7cos {\frac{x}{4}}-4sin {\frac{x}{2}}=4cos^3{\frac{x}{4}}[/tex]

[tex]7cos {\frac{x}{4}}-8 cos {\frac{x}{4}} sin {\frac{x}{4}}=4cos^3{\frac{x}{4}}[/tex]

[tex]cos {\frac{x}{4}}(4cos^2 {\frac{x}{4}}+8sin {\frac{x}{4}}-7)=0[/tex]

[tex]cos {\frac{x}{4}}(4(1-sin^2 {\frac{x}{4}})+8sin {\frac{x}{4}}-7)=0[/tex]

[tex]cos {\frac{x}{4}}(4sin^2 {\frac{x}{4}}-8sin {\frac{x}{4}}+3)=0[/tex]

[tex]4cos {\frac{x}{4}}(sin{\frac{x}{4}}-\frac{3}{2})(sin {\frac{x}{4}}-\frac{1}{2})=0[/tex]

3.[tex]sin^4 x +cos^4 x=sin 2x-\frac{1}{2}[/tex]

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

[tex]1-\frac{1}{2}sin^2 {2x}=sin 2x-\frac{1}{2}[/tex]

[tex]sin^2 {2x}+2sin 2x -3=0[/tex]

[tex](sin 2x-1)(sin 2x+3)=0[/tex]

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