Question

3sin^3(x)-4sinx+2√3=2√3cos^2(x)

Answer 1

sinx(4-3sin^2x)=2sqrt(3)(1-cos^2x)
sinx(4-3sin^2x)=2sqrt(3)sin^2x sinx=0 x=Пk
4-3sin^2x=2sqrt(3)sinx
sinx=y |y|<=1
3y^2+2sqrt(3)y-4=0
y=(-sqrt(3)+-sqrt(15))/3
y1=(sqrt(15)-sqrt(3))/3
y2=-sqrt(15)-sqrt(3)/3=-(sqrt(5)+1)/sqrt(3)<-1 не удовлетворяет
sinx=(sqrt(15)-sqrt(3))/3
x=(-1)^k*arcsin(sqrt(15)-sqrt(3))/3)+Пk