已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2).(1)求sina和tan2a的值
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![已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2).(1)求sina和tan2a的值](/uploads/image/z/1618255-55-5.jpg?t=%E5%B7%B2%E7%9F%A5sina%2Bcosa%3D3%E2%88%9A5%2F5%2Ca%E5%B1%9E%E4%BA%8E%280%2C%CF%80%2F4%29%2Csin%28%CE%B2-%CF%80%2F4%29%3D3%2F5%2C%CE%B2%E5%B1%9E%E4%BA%8E%EF%BC%88%CF%80%2F4%2C%CF%80%2F2%29.%281%29%E6%B1%82sina%E5%92%8Ctan2a%E7%9A%84%E5%80%BC)
已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2).(1)求sina和tan2a的值
已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2).(1)求sina和tan2a的值
已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2).(1)求sina和tan2a的值
sina=3√5/5-cosa ,sin^2a=9/5-6√5/5cosa+cos^2a=1-cos^2a ,
4/5-6√5/5cosa+2cos^2a=0 ,(2√5/5-cosa)(√5/5-cosa)=0 ,cosa= 2√5/5
sina=√5/5 ,tana=1/2
tan2a=2tana/(1-tan^2a)=1/(1-1/4)=4/3