Lol fair enough.
But that solution lacks rigour in my eyes. Without proper justification that both alpha and beta lie between -pi/2 and pi/2, cancelling out the tan's is not properly justified.
(Or it could be I'm too used to uni maths and everything has to be presented with 100% precision)
I'd be leaning towards saying that the solution would
probably be passable at this level of study, but I could be mistaken. The train of thought is solid enough
that being said, I recommend getting in the habit of writing all restrictions in the HSC, even those which are seemingly inconsequential or even obvious, to make the marker happy and to make sure your reasoning is clear, catch tricks, etc etc
you'd almost definitely get away with it, but better safe than sorry