α,β是锐角,sinα=4/5cos(α+β)=5/13,求sinβ?

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α,β是锐角,sinα=4/5cos(α+β)=5/13,求sinβ?
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α,β是锐角,sinα=4/5cos(α+β)=5/13,求sinβ?
α,β是锐角,sinα=4/5cos(α+β)=5/13,求sinβ?

α,β是锐角,sinα=4/5cos(α+β)=5/13,求sinβ?
cosα=3/5,sin(α+β)=12/13
cos(α+β)=cosαcosβ-sinαsinβ=3/5cosβ-4/5sinβ=5/13
sin(α+β)=sinαcosβ+cosαsinβ=4/5cosβ+3/5sinβ=12/13
可以解出sinβ=16/65

cos(a+b)=cosacosb-sinasinb 应该会了 吧

16/65
sinb = sin (a+b - a)= sin(a+b)cosa- cos(a+b)sina