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