已知5sinb=sin(2a+b) 求证 tan(a+b)/tana=3/2_数学解答

已知5sinb=sin(2a+b) 求证 tan(a+b)/tana=3/2

人气：113 ℃　时间：2020-02-04 10:41:59

解答

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