急求已知根号3sinθ-sin(π/2-2θ)/cos(π+θ)×cosθ=1 θ ∈(0,π) 求θ的值

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急求已知根号3sinθ-sin(π/2-2θ)/cos(π+θ)×cosθ=1 θ ∈(0,π) 求θ的值
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急求已知根号3sinθ-sin(π/2-2θ)/cos(π+θ)×cosθ=1 θ ∈(0,π) 求θ的值
急求已知根号3sinθ-sin(π/2-2θ)/cos(π+θ)×cosθ=1 θ ∈(0,π) 求θ的值

急求已知根号3sinθ-sin(π/2-2θ)/cos(π+θ)×cosθ=1 θ ∈(0,π) 求θ的值
∵sin(π/2-2θ)=sin(π/2)*cos(2θ)-cos(π/2)*sin(2θ)
=cos(2θ)=1-2*(sinθ)^2
又∵cos(π+θ)=cosπ*cosθ-sinπ*sinθ=-cosθ
∴原式子=√3sinθ+1-2*(sinθ)^2=1
∴2*sin²θ-√3sinθ=0
∴sinθ=0或√3/2
∵θ ∈(0,π),
∴θ=π/3 或2π/3