In △ ABC, if cot A, cot B, cot C be in A. P. then a2,b2,c2 are in
A.P.
cot A, cot B and cot C are in A.P.
⇒ cot A + cot C = 2 cot B ⇒cos Asin A+cos Csin C=2 cos Bsin B
⇒b2+c2−a22bc(ka)+a2+b2−c22ab(kc)=2a2+c2−b22ac(kb)
⇒ a2+c2=2b2. Hence a2,b2,c2 are in A. P.
It might help to remember this result as a general relation.