Question

Решите пожалуйста!
4(cos^2 (x/3) + sin (x/3))=1

Answer 1

4-4sin²(x/3)+sin(x/3)-1=0
4sin²(x/3)-sin(x/3)-3=0
sin(x/3)=a
4a²-a-3=0
D=1+48=49
a1=(1-7)/8=-3/4⇒sin(x/3)=-3/4⇒x/3=(-1)^n+1*arcsin3/4+πn⇒
x=(-1)^n+1*3arcsin3/4+3πn
a2=(1+7)/8=1⇒sin(x/3)=1⇒x/3=π/2+πn⇒x=3π/2+3πn

Answer 2

4a²-a-3=0
a₁=(1-7)/8=-3/4
sin(x/3)=-3/4
x/3=(-1)^n+arcsin3/4+πn
x=(-1)^n+3arcsin3/4+3πn
a₂=(1+7)/8=1
sin(x/3)=1
x/3=π/2+πn
x=3π/2+3πn