ok, so i think i have one of the implications down, but i'm having trouble with the converse. tell me if what i did is right so far.

Proof:

Assume x and y are the acute angles of a right triangle, then x + y = 90. This means that x and y are compliments. Recall that the sine of an angle is equal to the cosine of its compliment, and thus we can let cosy = sinx and cosx = siny.

Now sin(x + y) = sinxcosy + sinycosx = sinx(sinx) + siny(siny) = sin^2x + sin^2y

Now for the converse, we use the contrapositive. Assume sin(x + y) not= sin^2x + sin^2y....?