已知α属于【0,π/4】,β属于【0,π/4】且sin(2α+β)=3cos(α+β)sinα,4tanα/2=1-tan^α/2,求α+β的值
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![已知α属于【0,π/4】,β属于【0,π/4】且sin(2α+β)=3cos(α+β)sinα,4tanα/2=1-tan^α/2,求α+β的值](/uploads/image/z/13331795-59-5.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%E5%B1%9E%E4%BA%8E%E3%80%900%2C%CF%80%2F4%E3%80%91%2C%CE%B2%E5%B1%9E%E4%BA%8E%E3%80%900%2C%CF%80%2F4%E3%80%91%E4%B8%94sin%EF%BC%882%CE%B1%2B%CE%B2%EF%BC%89%3D3cos%EF%BC%88%CE%B1%2B%CE%B2%EF%BC%89sin%CE%B1%2C4tan%CE%B1%2F2%3D1-tan%5E%CE%B1%2F2%2C%E6%B1%82%CE%B1%2B%CE%B2%E7%9A%84%E5%80%BC)
已知α属于【0,π/4】,β属于【0,π/4】且sin(2α+β)=3cos(α+β)sinα,4tanα/2=1-tan^α/2,求α+β的值
已知α属于【0,π/4】,β属于【0,π/4】且sin(2α+β)=3cos(α+β)sinα,4tanα/2=1-tan^α/2,求α+β的值
已知α属于【0,π/4】,β属于【0,π/4】且sin(2α+β)=3cos(α+β)sinα,4tanα/2=1-tan^α/2,求α+β的值
sin(2α+β)=3cos(α+β)sinα
sin(α+β)cosα+cos(α+β)sinα=3cos(α+β)sinα
sin(α+β)cosα/cos(α+β)=2sinα/cosα
tan(α+β)=2tanα
4tanα/2=1-tan^α/2
2*2tanα/2/1-tan^α/2=1
tanα=1/2
tan(α+β)=2tanα=2*1/2=1
α属于【0,π/4】,β属于【0,π/4】
α+β属于【0,π/2】,
tan(α+β)=1
α+β=π/4