Задача 47864 4cos^3 x + 4sin^2 x = 1+3cosx...

vk321157147

2020-04-21 19:51:23

4cos^3 x + 4sin^2 x = 1+3cosx

azot

2020-04-21 20:48:15

4cos^(3) x + 4sin^(2) x = cos^(2)x+sin^(2)x+3cosx
4cos^(3) x + 3sin^(2 )x=cos^(2)x+3cosx
4cos^(3) x +3-3cos^(2)x=cos^(2)x+3cosx
4cos^(3) x-4cos^(2)x-3cosx+3=0
4cos^(2)x(cosx-1)-3(cosx-1)=0
(cosx-1)(4cos^(2)x-3)=0
1)cosx=1
[b]x1=2πn,n ∈ Z[/b]
2) 4cos^(2)x=3
cos^(2)x=3/4
cosx= ± sqrt(3)/2
[b]x2= ± π/6+πk, k ∈ Z[/b]