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If the function f defined on (π/6,π/3) by f(x) = {√2 cosx - 1/cot x - 1 x ≠ π/4 , f(x) = k, x = π/4

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If the function f defined on (π/6,π/3) by f(x) = {√2 cosx - 1/cot x - 1  x ≠ π/4 , f(x) = k, x = π/4 continuous, then k is equal to

(1)  1/√2

(2)  1

(3)  1/2

(4)  2

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Correct option  (1)  1/2

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