设α∈(0,π/3) β∈(π/6,π/2) 且5/3sinα+5cosα=8 /2sinβ+/6cosβ =2 求cos(α+β )/为根号/为5倍根号3 根号2 各号6

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设α∈(0,π/3) β∈(π/6,π/2) 且5/3sinα+5cosα=8 /2sinβ+/6cosβ =2 求cos(α+β )
/为根号
/为5倍根号3 根号2 各号6

5/3sinα+5cosα=10sin(α+π/6)=8
sin(α+π/6)=0.8; cos(α+π/6)=0.6
同理2sin(β+π/3)=/2 ;
2cos(β+π/3)=-/2
sin(α+β+π/2)=-0.1*/2
cos(α+β )=-0.1*/2