i'm too lazy to pull up how the teacher did this, it involves getting out ipad and i'm on spring break so screw it
it's probably really simple and i just don't want to think it through
it's fairly obvious to begin that the equation on the right is another way to express something of the form cos (x + y)
i also want to say that the dividing by h is probably just something to make it look complicated af and we can probably just multiply that and get that out of the way
if cos h - 1 = sin h so help me god
EDIT:
is confirmed that cos h - 1 does not equal sin h (logically)
but this introduces that the whole right part isn't actually some way to represent cos (x + y)...? after all, if
cos h - 1 does not equal sin h then that means what i typed in the previous sentence
i'll just sleep on it and figure it out in the morning or smh
or maybe i'm taking an entirely different look and because f(x) is apparently equal to cos x, i need to do something about that and simplify it for it to make sense
then that makes f(x + h) = cos x + h? which then makes the entire left part 1
1 = cos x ((cos h - 1) / h) - sin x (sin h / h)
ok sorry i'm way off now i bet lol