It's called a literal equation. The problem doesn't state which variable to solve for, but the assumption here is that it is x. Solving literal equations is a basic part of mathematics courses.
I'm a mathematician and I can't recall a time I've ever heard the term "literal equation." When I was in grade school the instructions were always "solve for x" if x was the variable being solved for.
I want to believe this is real, but I'm having trouble deciphering how one would "solve" this equation given no variable is referenced outside of the question and k is already isolated and terms simplified.
Considering the handwriting, it's probably all written by the same person. But even if it wasn't, it is very badly written if you had to solve it by making assumptions, imo.
I haven't had to do anything with sin, cos or tan in over 20 years and even back then it's a miracle I managed to pass my advanced math course considering I never understood what they were because it was so badly explained to us...