It's trigo time #7

So $x$ should equal to either 225 or 45 because:

$tan\ 45=1$ and $tan\ 225=1$

So our answer is

225 or 45

Relevant wiki: Half Angle Tangent Substitution

$\begin{aligned} \frac {\cos x(1+\tan^2 x)}{\csc x} & = 1 & \small \color{#3D99F6} \text{Note that } \csc x = \frac 1{\sin x} \\ \sin x \cos x(1+\tan^2 x) & = 1 & \small \color{#3D99F6} \text{And } \sin 2x = 2 \sin x \cos x \\ \frac 12 {\color{#3D99F6} \sin 2x} (1+\tan^2 x) & = 1 & \small \color{#3D99F6} \text{Using half-angle tangent substitution} \\ \frac 12 \cdot {\color{#3D99F6} \frac {2\tan x}{1+\tan^2 x}} \cdot (1+\tan^2 x) & = 1 \\ \tan x & = 1 \\ \implies x & = \boxed{45^\circ \text { or } 225^\circ} \end{aligned}$