Question

三角怎么变换成下面的变成

Answer 1

主要是二倍角公式.

分子 = (1-cosx)+sinx = 2[sin(x/2)]^2+2sin(x/2)cos(x/2) = 2sin(x/2)*[sin(x/2)+cos(x/2)] ,

分母 =(1+cosx)+sinx = 2[cos(x/2)]^2+2sin(x/2)cos(x/2) = 2cos(x/2)*[cos(x/2)+sin(x/2)] ,

约分后,左边 = sin(x/2) / cos(x/2) = tan(x/2) .