How do i justify my steps when simplifying?

You justify a step the same way you decided to go through with it:
Remember a rule, axiom, postulate, theorem, or corollary you learned
that says it's a legal thing to do.

Like if you thought of erasing one of the terms in an equation because
that would make the rest of the equation easier to work with, you would
not do that, because no book or teacher ever said that it was legal.

Or if you thought of adding 42 to both sides of an equation, you could
do that, because you learned that "If equals are added to equals, then
the results are equal".  Then later, if anybody ever asked you why you
could do that, or asked you to justify your step, you'd tell them the same
statement.

We use the identity  sin (A - B) = sin A cos B - cos B sin A

so the above  = sin (11pi/12 -  pi/6) = sin 3pi/4 =  1 / sqrt2 answer