cot¯¹ n/ΠΠ/6 n belongs to natural numbers, then the maximum value of n is (a) 1 (b) 5 (c) -5 (d) none of these

Question

cot&macr;&sup1; n/&Pi;>&Pi;/6 n belongs to natural numbers, then the maximum value of n is (a) 1 (b) 5 (c) -5 (d) none of these

Ramesh V · Answer

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

A B · Answer

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

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