Cot(a).cot(60+a).cot(60-a)=????????????????????????????

 

Dear Himanshu

 

it can be written as 1/ [ tan A tan (60-A) tan (60+A)] =1/ tan 3A

 

hence = cot 3A

 

Hope it helps

 

In case of any difficulty, please feel free to ask.

Cota.Cot(60+a).Cot(60-a) =cosa.cos(60+a)cos(60-a)/sina.sin(60+a)sin(60-a)=cosa{2cos(60+a).cos(60-a)}/sina{2sin(60+a)sin(60-a)} =cosa.(cos2a+cos120)/sina(cos2a-cos120)=cosa.cos2a+cosa.cos120/sina.cos2a-sina.cos120=2cosa.cos2a-cosa/2sina.cos2a+sina=cosa+cos3a-cosa/sin3a-sina+sina=cos3a/sin3a=cot3a