已知sinα=2/3,α∈(π/20,π),求cos(π/3+α),cos(π/3-α)
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![已知sinα=2/3,α∈(π/20,π),求cos(π/3+α),cos(π/3-α)](/uploads/image/z/11561521-49-1.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B1%3D2%2F3%2C%CE%B1%E2%88%88%EF%BC%88%CF%80%2F20%2C%CF%80%EF%BC%89%2C%E6%B1%82cos%EF%BC%88%CF%80%2F3%2B%CE%B1%EF%BC%89%2Ccos%EF%BC%88%CF%80%2F3-%CE%B1%EF%BC%89)
已知sinα=2/3,α∈(π/20,π),求cos(π/3+α),cos(π/3-α)
已知sinα=2/3,α∈(π/20,π),求cos(π/3+α),cos(π/3-α)
已知sinα=2/3,α∈(π/20,π),求cos(π/3+α),cos(π/3-α)
sin(π-α)=sinα=2/3;
α∈(π/2,π),
则cosα=-√(1-(sinα)^2)=-√5/3.
α/2∈(π/4,π/2)
∴sinα/2=√[(1-cosα)/2]
=√[(1+√5/3)/2]
=(分子有理化,可化简)