Are there multiple ways to verify a trig identity?

[Mark44]

That makes plenty of sense

When I think about, it's not that difficult to determine whether a move is legit or not.

No, it's not. If the operation you apply to both sides of an equation is one-to-one, it's reversible. For example, adding a number to or subtracting a number from each side, multiplying each side by a nonzero number, and exponentiating each side are reversible operations. In contrast, squaring both sides of an equation is not reversible.

 

[Vanadium 50]

When I think about, it's not that difficult to determine whether a move is legit or not.

If you do these by operating on only one side - the way trig has traditionally been taught - it's automatic.