Question 7
Prove that for all real numbers $x \in \left(-\frac{3\pi}{2}, \frac{\pi}{2}\right)$ the equality
$$
\frac{2}{1 - \sin x} = \tan^2 \left( \frac{x}{2} + \frac{\pi}{4} \right) + 1
$$
holds.
$$
\frac{2}{1 - \sin x} = \tan^2 \left( \frac{x}{2} + \frac{\pi}{4} \right) + 1
$$
holds.