化简：cos^2x / ( cot(x/2)-tan(x/2) )

题目

化简：cos^2x / ( cot(x/2)-tan(x/2) )

答案

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