If cot x + cosec x = √3 , then the principal value of (x - π/6)

1) π/3

2) π/4

3) π/2

4) π/6

Answer: (4) π/6

Solution:

Given,

cot x + cosec x = √3

(cos x/sin x) + (1/sin x) = √3

(cos x + 1)/sin x = √3

2 cos2(x/2)/ [2 sin (x/2) cos (x/2)] = √3

cos (x/2)/ sin (x/2) = √3

cot (x/2) = √3

Or

tan (x/2) = 1/√3

x/2 = nπ + π/6

x = 2nπ + π/3

x – π/6 = 2nπ + π/6

The principal value of x – π/6 for n = 0 is π/6.

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