Can I divide both sides by tan(x)?

It shows that $\tan x$ can't/doesn't equal 0, not just $x$. It's an important distinction.

I think I understand. It takes a while for some of these math concepts to really sink in : / but it's definitely clearer now.

What are you final solutions?

Do you mean which A-level module?

No, for this question, what are the final answers you get?

Ah, haha. I get x= π/4 , π3/4

Yep!

I understand almost everything, but once in a while something comes up which I don't understand and I want to understand - instead of just accepting it. That could cause problems in the exams, if I don't understand exactly how it works.

Tbh, I may have made a mistake. I'm a "mature" student (34) and I really wanted to get out of my job this year and to a university degree/master's I want. One of my options wanted this a-level. So I entered myself for the exams before I'd learned much of the maths. I've quit almost all my work hours and learned nearly half the A-level maths, but there's still about 1 1/2 months til the first math exams. I'm getting a bit panicky now. I may have been a bit rash in registering myself.

In any case, many thanks for your help! It helps me a lot.

Oh, that's admirable. I did something similar, although I'm seventeen, I quit school and self-taught myself A-Level Maths, Further Maths and Physics in 3 months and sat the exams this Jan. If I can do it, then so can you. I know that feeling of panic all too well, but you just gotta keep your cool and it'll end up fine.

Good luck!