sinA=4/5 cos(A+B)=5/13 求sinB

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sinA=4/5 cos(A+B)=5/13 求sinB
sinA=4/5 cos(A+B)=5/13 求sinB

sinA=4/5 cos(A+B)=5/13 求sinB
a,b都是锐角
所以0所以sina>0,sin(a+b)>0
sinb
=sin((a+b)-a)
=sin(a+b)cosa-cos(a+b)sina
=12/13*3/5-5/13*4/5
=16/65

sinB=sin(B+A-A)=sin(B+A)cosA-cos(B+A)sinB
这样分类讨论就可以算出来了,我算了下,应该是-56/65

sin(A+B)=sinAcosB+cosAsinB
11/13=(4/5)cosB+(3/5)sinB (1)
cos(A+B)=cosAcosB-sinAsinB
5/13=(3/5)cosB-(4/5)sinB (2)
from 3(1)- 4(2)
sinB= 1/5