Yes,

because tan is sine divided by cosine.

You could also do what

recommended,

which is to use the identity for Cos(A-B) and also Sin(A-B) for the tan and cotan, working from there.

In using an arbitrary value, you are proving the equation for that value only,

not in general.

You should go the extra mile and either draw the right-angled triangle

or use identities as

recommended.

Your original answers to numbers 2. and 3. were correct,

however I'd recommend you work on them a bit more.

I have to go to sleep but I will continue with this tomorrow,

in the meantime try.