Question

Для каждого значения параметра а решите уравнение

 

 

2 sin^3x+sin2xcosx=6a-4

 

Answer 1

2sin^3x+2sinxco^2x=6a-4

2sinx(sin^2x+cos^2x)=6a-4

sinx=3a-2

|3a-2|<=1

3a-2<=1

a<=1  3a-2>=0  a>=2/3  [2/3;1]

2-3a<=1  a>=1/3  a<2/3

a [1/3;1]

x=arcsin(3a-2)+2Пk

Answer 2

2sin^3 x + sin2xcosx = 6a-4

2sin^3 x + 2sinx * cosx * cosx = 6a-4

2sinx(sin^2 x + cos^2 x) = 6a - 4

sinx = 3a -2

-1<= 3a-2<=1

-1 <= 3a -2

1/3 <=a

3a -2<=1

a=<1

a= [1/3 ; 1]