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If $y = \log_e \tan \left(\frac{\pi}{4} + \frac{x}{2}\right)$,then $\tanh \left(\frac{y}{2}\right) = $

Which one of the following is possible?

$\frac{1+\tanh \left(\frac{x}{2}\right)}{1-\tanh \left(\frac{x}{2}\right)} = $

$\frac{\sin \theta}{1-\cot \theta} + \frac{\cos \theta}{1-\tan \theta} = $

The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x = \frac{1}{4}$ are $.......$

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