已知α、β是锐角,且sinα=(4√3)/7,cos(α+β)=-11/14,求sinβ的值(过程)

已知α、β是锐角,且sinα=(4√3)/7,cos(α+β)=-11/14,求sinβ的值(过程)
已知α、β是锐角,且sinα=(4√3)/7,cos(α+β)=-11/14,求sinβ的值(过程)

已知α、β是锐角,且sinα=(4√3)/7,cos(α+β)=-11/14,求sinβ的值(过程)
sina=4根号3/7 ,cosa=1/7
cos(a+b)=-11/14,sin(a+b)=5根号3/14
sin(b)
=sin(a+b-a)
=sin(a+b)cosa-sinacos(a+b)
=5根号3/14×1/7-4根号3/7×(-11/14)
=(5根号3+44根号3)/(7×14)
=根号3/2
b是锐角,所以b=派/3

sinα=(4√3)/7，则cosa=1/7
cos(α+β)=-11/14,则sin(a+β)=(5√3)/14
sinβ
=sin(a+β-a)
=sin(a+β)cosa-cos(a+β)sina
=(5√3)/14*1/7+11/14*(4√3)/7
=√3/2