I was taught that (and pretty sure that for the HSC):
"Prove that" questions: you can start off with LHS or RHS. You could even work on both sides and show that they are equal, although it's not recommended if not necessary.
"Show that" questions: you can only start off with LHS.
... however this seems to go against RuiAce's guide Verbs and Maths.
Yeah, they don't make that distinction at the HSC level, prove and show are for all purposes identical
When proving that:
(sin^2x tanx) + (cos^2x cotx) + 2sinxcox = tanx + cotx
Assuming that factorised it correctly (tbh, I sort of bludged it through brute force...), is it allowed to skip to:
(sin^2x + cos^2x)(tanx +cotx)
Or do you have to show the whole working out from A to B?
Hey pancakes! In this case, I would say that's a tad few steps to skip. If you are doing it anyway, you might as well write it down! Especially in proof questions, where the marker needs to verify that you didn't just fudge steps based on a guess/intuition, it's best to show all but the most trivial steps
in this case, try and show how you got to that next result; you've skipped virtually all of the hard work