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
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![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](/uploads/image/z/1786626-18-6.jpg?t=%E5%B7%B2%E7%9F%A5tanB%3D4%2F3%2Csin%28a%2BB%EF%BC%89%3D5%2F13%E4%B8%94a%2CB%E2%88%88%280%2C%CF%80%29%2C%E5%88%99sina%E7%9A%84%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91%3F%E6%B1%82%E8%AF%A6%E8%A7%A3)
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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