cot¯¹ n/Π>Π/6 n belongs to natural numbers, then the maximum value of n is

(a) 1

(b) 5

(c) -5

(d) none of these

From the graph ,we can see that cot x is periodic function with period as  Π .

hence ,cot¯^¹ n/Π > Π/6  can be found only for ( 0 , Π )

                       n/Π > cot Π/6

                       n/Π > 3^1/2

                       n >  Π.3^1/2

                       n > 5.43  or n>=6  

answer: none of these

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regards

Ramesh

Actually since cos is a decreasing function for the specified range therefore n