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If $x + i y = \frac{1}{1 - \cos θ + 2 i \sin θ}, θ \neq 2 n π, n \in I$ then maximum value of x is

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Correct option is C

2x=(x+iy)+(x−iy)=2(1−cos⁡θ)(1−cos⁡θ)2+4sin2⁡θ⇒ x=15+3cos⁡θThus, maximum value of x is 12. It is attained at θ =π.

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If x+iy=11−cos⁡θ+2isin⁡θ,θ≠2nπ,n∈I then maximum value of x is

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If $x + i y = \frac{1}{1 - \cos θ + 2 i \sin θ}, θ \neq 2 n π, n \in I$ then maximum value of x is