Question

求证cos^2a/cota/2-tana/2=1/4sin2a

Answer 1

先看分母:cot(a/2)-tan(a/2)=cos(a/2)/sin(a/2)-sin(a/2)/cos(a/2) =(cos^2(a/2)-sin^2(a/2))/(sin(a/2)cos(a/2)) =cosa/(sin(a/2)cos(a/2)) =2cosa/sina 所以：cos^2a/(cot(a/2)-tan(a/2))=cosasina/2=sin2a/4