设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,则cosβ=?

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设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,则cosβ=?设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,则cosβ=?设α,β均为锐角,cosα=1/7,co

设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,则cosβ=?
设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,则cosβ=?

设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,则cosβ=?
设α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,
则cosβ=cos(α+β-α)=cos(α+β)cosα)+sin(α+β)sinα
=(-8/17)(1/7)+(15/17)(4根号3)/7
=-8/119+60(根号3)/119=[-8+60(根号3)]/119
(由于:知:0

α,β均为锐角,cosα=1/7,cos(α+β)=-8/17,所以sinα=4√3/7
cosβ=cos[(α+β)-α ]=cos(α+β)cosα+sin(α+β)sinβ=-8/17 乘以1/7 +15/17 乘以4√3/7
= -8+60√3
 ̄ ̄ ̄
119