The maximum value of (cos α1) (cot α2) …….. (cot αn) = 1 is
1nn2
From the given relations we have
∏ni=1(cos αi)=∏ni=1(sin α1)⇒∏ni=1(cos αi)=∏ni=1(cos αi sin α1)=∏ni=1(sin 2αi2)
Since 0≤α1≤12" and max. value of sin 2α, is 1 for all i. ∏ni=1(cos αi)=12n2