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sin3θ=3sinθ-4sin^3θ用几何求证求快答

题目详情
sin3θ=3sinθ-4sin^3 θ用几何求证
求快答
▼优质解答
答案和解析
左=sin3θ
=sin(2θ+θ)
=sin2θcosθ+cos2θsinθ
=2sinθcos²θ+(1-2sin²θ)sinθ
=2sinθcos²θ+sinθ-2sin³θ
=2sinθ(cos²θ-sin²θ)+sinθ
=2sinθ(1-2sin²θ)+sinθ
=2sinθ-4sin³θ+sinθ
=3sinθ-4sin³θ=右