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учечик
@учечик
August 2022
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помогите решить тригонометрическое уравнение №4
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sedinalana
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2сos²(2x+π/3)-(1-cos(2x+π/3))/2=2
4cos²(2x+π/3)-1+cos(2x+π/3)-4=0
cos(2x+π/3)=a
4a²+a-5=0
D=1+80=81
a1=(-1-9)/8=-1,25⇒cos(2x+π/3)=-1,25<-1 нет решения
a2=(-1+9)/8=1⇒cos(2x+π/3)=1⇒2x+π/3=2πn⇒2x=-π/3+2πn⇒
x=-π/6+πn,n∈z
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учечик
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Answers & Comments
Verified answer
2сos²(2x+π/3)-(1-cos(2x+π/3))/2=24cos²(2x+π/3)-1+cos(2x+π/3)-4=0
cos(2x+π/3)=a
4a²+a-5=0
D=1+80=81
a1=(-1-9)/8=-1,25⇒cos(2x+π/3)=-1,25<-1 нет решения
a2=(-1+9)/8=1⇒cos(2x+π/3)=1⇒2x+π/3=2πn⇒2x=-π/3+2πn⇒
x=-π/6+πn,n∈z