Для каждого значения параметра а решите уравнение
2 sin^3x+sin2xcosx=6a-4
2sin^3x+2sinxco^2x=6a-4
2sinx(sin^2x+cos^2x)=6a-4
sinx=3a-2
|3a-2|<=1</p>
3a-2<=1</p>
a<=1 3a-2>=0 a>=2/3 [2/3;1]
2-3a<=1 a>=1/3 a<2/3</p>
a [1/3;1]
x=arcsin(3a-2)+2Пk
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</p>
-1 <= 3a -2</p>
1/3 <=a</p>
3a -2<=1</p>
a=<1</p>
a= [1/3 ; 1]