The question says find the exact value of:
sin 67.5
This is a double angle identity question and I think im getting confused because its actually a half angle (135/2).
I have to use sin(2A) = 2sin(A)cos(A)
(I know there is a half angle formula, but our teacher never taught us that and he said we should be able to do it with the sine double angle formula anyway)
trust me, the double angle formula is way more trouble than it's worth here. i thin it's far more likely that your professor expects you to study ahead rather than apply the double angle formula.
note that
now you have to know what quadrant the original angle is in in order to know if it should be a plus or minus