Can anybody please help me with this derivatives problem about graphs?

Question

Show that the curves y= e^(-x) and y= -e^(-x) touch the curve
y=e^(-x)*sinx at its inflection points.

Answer 1

That's the same thing as saying that sin x = +1 or -1 at the inflection points.

But

y' = e^(-x) * (cosx - sinx)
y'' = (e^(-x) * (-sinx - cosx - (cos x - sin x)) = -2cosx e^(-x)

That equals 0 when and only when cos x does. But when cos = 0, what does sin = ??