已知1-tana/2+tana=1 求证:tan2a=-4tan(a+π/4)
问题描述：
已知1-tana/2+tana=1 求证:tan2a=-4tan(a+π/4)
答
1-tana/2+tana=1 1-tana=2+tana tana=-1/2所以tan2a=2tana/(1-tan²a)=-4/3tan(A+π/4)=(tanA+tanπ/4)/(1-tanAtanπ/4)=(-1/2+1)/(1-(-1/2))=1/3所以tan2a=-4tan(a+π/4)