The question asks to solve, in the interval $-180° \leq x < 180°$, the equation:
$$\sin x (\cos x + \csc x) = 2 \cos^2 (x)$$
This equation simplifies to
$$\tan 2x = 2$$
According to this, $2x$ (with a domain multiplied by $2$ to become $-360° \leq x < 360°$) must be the following: $63.43°, 243.43°, -116.57°,$ and $-296.57°$. And therefore, after dividing by $2$, x must be: $31.7°, 121.7°, -58.3°, -148.3°$
However, the answer excludes these two: $121.7°$ and $-148.3°$
I don't understand why.