已知cos(π/2-α)=√2cos(3π/2+β),√3sin(3π/2-α)=-√2sin(π/2+β),且α,β∈(0,π),求α,β的值

已知cos(π/2-α)=√2cos(3π/2+β),√3sin(3π/2-α)=-√2sin(π/2+β),且α,β∈(0,π),求α,β的值
已知cos(π/2-α)=√2cos(3π/2+β),√3sin(3π/2-α)=-√2sin(π/2+β),且α,β∈(0,π),求α,β的值

已知cos(π/2-α)=√2cos(3π/2+β),√3sin(3π/2-α)=-√2sin(π/2+β),且α,β∈(0,π),求α,β的值
由cos(π/2-α)=√2cos(3π/2+β）,得sinα=√2sinβ,(1)
√3sin(3π/2-α)=-√2sin(π/2+β),得√3cosα=√2cosβ,(2)
根据cosα的平方+sinα的平方=1且cosβ的平方+sinβ的平方=1
得cosα的平方*2=1,cosα==正负√2/2 α=π/4或3π/4
由 (2)得 当α=π/4 时,β=π/3
当α=3π/4 时,β=2π/3