If the expression $\frac{s i n x / 2 + c o s x / 2 - i t a n x}{1 + 2 i s i n x / 2}$ is real, then the set of all possible values of x is ...................

n π / 4

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n π / 2

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n π

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2 n π

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Solution

The correct option is D $2 n π$
The above expression will be real if imaginary part is 0.
Thus
$t a n (x) = 0$
$x = n π$ ...(i)
And
$s i n (\frac{x}{2}) = 0$
$\frac{x}{2} = n π$
$x = 2 n π$ ...(ii)
Hence
From i and ii, we get the solution as $2 n π$ . where $n ϵ N$

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