Help with simplest form sin(2pift - pi) + sin(2pift + pi)

Answer 1

Not sure what the f is doing in there, but recall that

sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)

I think you got too many π's floating around in there, as well.

sin(x+π) = sin(x-π) = -sin(x)

Answer 2

It occurred to me this might be a physics problem:

sin(ωt-π)+sin(ωt+π)
= -2sin(ωt)