We are given that, (cot‌α1).(cot‌α2).....(cot‌αn)=1 ⇒ (cos‌α1.(cos‌α2)....(cos‌αn)=(sin‌α1).(sin‌α2)......(sin‌αn) ...(i) Let y=(cos‌α1).(cos‌α2)....(cos‌αn) (to be max.) Squarring both sides, we get y2=(cos2α1).(cos2α2).....(cos2αn) =cos‌α1.sin‌α1.cos‌α2.sin‌α2.cos‌αn.sin‌αn [using (i)] =
1
2n
[sin‌2‌α1.sin‌2‌α2......sin‌2‌αn] As 0≤α1,α2,......,αn≤