sin(θ+π/3)=3/5 θ∈(π/6,2π/3)则cosθ=

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sin(θ+π/3)=3/5 θ∈(π/6,2π/3)则cosθ=
sin(θ+π/3)=3/5 θ∈(π/6,2π/3)则cosθ=

sin(θ+π/3)=3/5 θ∈(π/6,2π/3)则cosθ=
sin(θ+π/3)=3/5
cos(θ+π/3)=-4/5
sinθ1/2+cosθ√3/2=3/5
sinθ√3/2+cosθ3/2=3√3/5
cosθ1/2-sinθ√3/2=-4/5
cosθ3/2+cosθ1/2=3√3/5-4/5
2cosθ=(3√3-4)/5
cosθ=(3√3-4)/10

【1】30<x<120.===>90<x+60<180.结合sin(x+60)=3/5,可得cos(x+60)=-4/5.【2】cosx=cos[(x+60)-60]=cos(x+60)cos60+sin(x+60)sin60=(-4/5)×(1/2)+(4/5)×(√3/2)=(-2+2√3)/5.∴cosx=2(-1+√3)/5.