asymptotes of the graph

x = \frac{3 π}{2}

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x = - \frac{π}{2}

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x = \frac{π}{2}

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x = - \frac{3 π}{2}

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Solution

The correct options are
A $x = \frac{3 π}{2}$
B $x = - \frac{π}{2}$
$f^{'} (x) = \frac{cos (x)}{1 + sin (x)}$
Or
$\frac{d y}{d x} = \frac{cos x}{1 + sin x}$
For asymptotes,
$\frac{d y}{d x} = \infty$
Or
$d x = 0$
Or
$sin (x) = - 1$
Or
$x = \frac{3 π}{2}, \frac{- π}{2}$ .

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