Question

2cosa+sina =根号5,求sina,cosa

Answer 1

令sinβ=2/√5,

2cosα+sinα=√5（cosα*2/√5+sinα*1/√5)=√5,

cosαsinβ+cosβsinα=1,

sin(α+β)=1=sin（π/2）,

α+β=π/2,α=π/2-β,

sinα=sin(π/2-β)=cosβ=1/√5=√5/5,

cosα=cos(π/2-β)=sinβ=2/√5=2√5/5.

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