1)[latex] \frac{sin70+sin20}{cos35+ \sqrt{3}sin35 } [/latex]2)[latex] \sqrt{3}sin2x+2cos^2x-1=2sinx [/latex]3)[latex]2+cos2x меньше 3cosx[/latex]4)[latex] \frac{1-4sin^2x}{cos2x+1} \leq 2[/latex]

Question

1)[latex] \frac{sin70+sin20}{cos35+ \sqrt{3}sin35 } [/latex]2)[latex] \sqrt{3}sin2x+2cos^2x-1=2sinx [/latex]3)[latex]2+cos2x меньше 3cosx[/latex]4)[latex] \frac{1-4sin^2x}{cos2x+1} \leq 2[/latex]

1)[latex] \frac{sin70+sin20}{cos35+ \sqrt{3}sin35 } [/latex] 2)[latex] \sqrt{3}sin2x+2cos^2x-1=2sinx [/latex] 3)[latex]2+cos2x<3cosx[/latex] 4)[latex] \frac{1-4sin^2x}{cos2x+1} \leq 2[/latex]

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Accepted Answer

4) ОДЗ cos2x≠0 x≠π2 1-4sin²x≤2(cos2x+1) 1-4sin²x≤4-2sin²x 2sin²x-3≤0 2(sinx+√3/2)(sinx-√3/2)≤0 sinx∈[-√3/2; √3/2] x∈[-π/6; +π/6] 3) 2+cos2x≤3cosx-1 2cos²x-3cosx+1≤0 Через Дискриминант пусть cosx=a и т.д. 2(cosx-1/2)(cosx-1)≤0 cosx∈[1/2; 1] x∈[0; π/3]