Question

已知7sina=3sin(a+b),求证 2tan2a+b/2=5tanb/2

Answer 1

利用合分比定理得,

7sina=3sin(a+b)-->sin(a+b)/sina=7/3

-->[sin(a+b)+sina]/[sin(a+b)-sina]=(7+3)/(7-3)

分子分母和差化积得

-->[2sin(a+b/2)cosb/2]/[2cos(a+b/2)sinb/2]=5/2-

-->tan(a+b/2)/tanb/2=5/2

--->2tan[(2a+b)/2]=5tan(b/2)