Question

Помогите решить задание по тригонометрии

Answer 1

4sin^3(x)-3sin(x)+2cos(2x)+1=0

4sin^3(x)-3sin(x)+2-4sin^2(x)+1=0

4sin^2(x)*(sin(x)-1)-3(sin(x)-1)=0

(sin(x)-1)*(4sin^2(x)-3)=0

sin(x)-1=0            или     4sin^2(x)-3=0

sin(x)=1                            4sin^2(x)=3

x1=(pi/2)+2pi*n, n=Z        sin^2(x)=3/4

                                            sin(x)=sgrt(3)/2

                                            x2=((-1)^k)*arcsin(sgrt(3)/2)+pi*k ,   k=Z

                                            x2=((-1)^k)*(pi/3)+pi*k, k=Z