已知5根号3sinα+5cosα=6根号2sinβ+根号6cosβ=1,且α∈(0,π/3),β∈(π/6,π/2),求cos(α+β)的值

已知5根号3sinα+5cosα=6根号2sinβ+根号6cosβ=1,且α∈(0,π/3),β∈(π/6,π/2),求cos(α+β)的值
已知5根号3sinα+5cosα=6根号2sinβ+根号6cosβ=1,且α∈(0,π/3),β∈(π/6,π/2),求cos(α+β)的值

已知5根号3sinα+5cosα=6根号2sinβ+根号6cosβ=1,且α∈(0,π/3),β∈(π/6,π/2),求cos(α+β)的值
5根号3sinα+5cosα = 10 sin(α + pai/6) =1
sin(α + pai/6) = 1/10
α = arcsin(1/10) - pai/6
你确定α∈(0,π/3）吗?
6根号2sinβ+根号6cosβ= 根号（78）sin(β+T) = 1,T = arctan 根号（3）/6