Предмет: Алгебра, автор: dasha3dasha

4 cos x = 4 - sin²x , решите кто сможет, пожалуйста)) буду очень признательна)

Ответы

Автор ответа: русская25

4 cos x = 4 - sin²x
4cosx + sin²x - 4 =0
4cosx + (1 - cos²x) - 4 =0
-cos²x+4cosx - 3 =0 |*(-1)
cos²x - 4cosx + 3 =0
Замена: cosx=t
t² - 4t + 3 =0
D= 16 - 4*1*3 = 16 - 12 = 4
t₁ = 4+2/2 = 3
t₂= 4-2/2 = 1

cosx=3 - нет решения,т.к -1≤cosx≤1

cosx= 1
x= 2πn, n∈z

Ответ: 2πn, n∈z.

Автор ответа: marat72

4cosx=4-sin^2x
4=4sin^2x+4cos^2x
4cosx=3sin^2x+4cos^2x
4cos^2x+3-3cos^2x-4cosx=0 cosx=t
t^2-4t+3=0
D1=4-3=1
Т1,2=2+-1=3;1
cosx=3 невозможно (cos принимает значения от -1 до 1)
cosx=1
х=2Пn,n принадлежит целым

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