The equation to solve is \( \csc(2x) = k \). This can be transformed into:
\[ \csc(2x) = \frac{1}{\sin(2x)} \Rightarrow \sin(2x) = \frac{1}{k} \]
Cosecant (\( \csc \)) is the reciprocal of the sine function.
Sine (\( \sin \)) is a trigonometric function of an angle.
To solve \( \csc(2x) = k \), we first find the angle for which \( \sin(2x) = \frac{1}{k} \).
The general solutions are:
Thus, \( x \) can be found by dividing each solution by 2.