若sinB=m*sin(2A+B),其中M不为1,角A不等于90度的倍数,求证:tan(A+B)=(1+m)/(1-m)*tanA
问题描述：
若sinB=m*sin(2A+B),其中M不为1,角A不等于90度的倍数,求证:tan(A+B)=(1+m)/(1-m)*tanA
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答
sinB=m*sin(2A+B)m=sinB/sin(2A+B)1+m=[sin(2A+B)+sinB]/sin(2A+B)=2[sin(A+B)cosA]/sin(2A+B)1-m=[sin(2A+B)-sinB]/sin(2A+B)=2[cos(A+B)sinA]/sin(2A+B)(1+m)/(1-m)=[sin(A+B)cosA]/[cos(A+B)sinA]=tan(A+B)/tanAt...