已知tanB=4/3,sin(a+B）=5/13且a,B∈(0,π),则sina的值为多少?求详解

已知tanB=4/3,sin(a+B）=5/13且a,B∈(0,π),则sina的值为多少?求详解
已知tanB=4/3,sin(a+B）=5/13且a,B∈(0,π),则sina的值为多少?求详解

已知tanB=4/3,sin(a+B）=5/13且a,B∈(0,π),则sina的值为多少?求详解
tanb=4/3 b∈(0,π),得
sinb=4/5 cosb=3/5
sin(a+b）=5/13且a,b∈(0,π)得
cos(a+b)=-12/13
于是
sina=sin(a+b-b)
=sin(a+b)cosb-cos(a+b)sinb
=5/13×3/5+12/13×4/5
=15/65+48/65
=63/65