The sum of solutions of the equation $\frac{\cos x}{1 + \sin x} = | \tan 2 x |, x \in (- \frac{π}{2}, \frac{π}{2}) - \{\frac{π}{4}, \frac{- π}{4}\}$ is

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$\frac{- 7 π}{30}$

$\frac{- π}{15}$

$\frac{π}{10}$

$\frac{- 11 π}{30}$

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Detailed Solution

$\frac{\cos x}{1 + \sin x} = | \tan 2 x |, x \in (- \frac{π}{2}, \frac{π}{2}) - \{\frac{π}{4}, \frac{- π}{4}\}$
$\begin{array}{l} \frac{\cos^{2} \frac{x}{2} - \sin^{2} \frac{x}{2}}{{(\cos \frac{x}{2} + \sin \frac{x}{2})}^{2}} = | \tan 2 x | \Rightarrow \tan (\frac{π}{4} - \frac{x}{2}) = |\tan 2 x| \Rightarrow \tan^{2} (\frac{π}{4} - \frac{x}{2}) = \tan^{2} 2 x \\ \Rightarrow x = \frac{- 3 π}{10}, \frac{- π}{6}, \frac{π}{10} \end{array}$