化简：cos^2x / ( cot(x/2)-tan(x/2) )
问题描述：
化简：cos^2x / ( cot(x/2)-tan(x/2) )
答
sin(x/2)cos(x/2)cos(x)
答
=cos²x(tan(x/2) / [ 1-tan²(x/2)] )
=cos²xtanx/2
=cosxsinx/2
=sin(2x)/4
答
令a=x/2则x=2a原式= cos²2a/(cosa/sina-sina/cosa)=cos²2a/[(cos²a-sin²a)/sinacosa]=cos²2a/[cos2a/sinacosa]=sinacosacos2a=1/2*sin2acos2a=1/4*sin4a=1/4*sin2x