高一数学：已知5sinB=sin(2A+B),求tan(A+B)cotB的值急!
问题描述：
高一数学：已知5sinB=sin(2A+B),求tan(A+B)cotB的值
急!
答
5sinB = sin(2A+B) = sin(A+B +A) = sin(A+B)cosA + cos(A+B)sinA,
sinB = sin(A+B-A) = sin(A+B)cosA - cos(A+B)sinA
5sin(A+B)cosA - 5cos(A+B)sinA = sin(A+B)cosA + cos(A+B)sinA
4sin(A+B)cosA = 6cos(A+B)sinA,
tan(A+B)cotA = 6/4 = 3/2
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是cotA吧.