已知sina+cosa=3√5/5,α属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2)(1)求
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已知sina+cosa=3√5/5,α属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2)(1)求sin2a和tan2a的值
![已知sina+cosa=3√5/5,α属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2)(1)求](/uploads/image/z/4446573-69-3.jpg?t=%E5%B7%B2%E7%9F%A5sina%2Bcosa%3D3%E2%88%9A5%2F5%2C%CE%B1%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%28%CF%80%2F4%2C%CF%80%2F2%29%281%29%E6%B1%82)
1.两边平方:(sina + cosa)^2 =(sina)^2 + 2sina*cosa + (cosa)^2 = 1 + sin2a =9/5
∴sin2a=4/5
∵a∈(0,π/4)
∴2a∈(0,π/2)
∴cos2a=√[1 - (sin2a)^2] = 3/5
tan2a=4/3
∴sin2a=4/5
∵a∈(0,π/4)
∴2a∈(0,π/2)
∴cos2a=√[1 - (sin2a)^2] = 3/5
tan2a=4/3
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