Does anyone know this?

First it is important to know that the sine of an angle is the fraction of the opposite side over the hypotenuse side, while cosine is the adjacent over the hypotenuse and finally tangent is opposite over adjacent. You can't take the sine, cosine or tangent of the right angle like this though.

sine is o/h

cosine is a/h

tangent is o/a

So let's do each angle.

Keep in mind E is the right angle so we can't take any trig function of it with SOH CAH TOA so let's do D first.

D has an adjacent side of f since e is the hypotenuse, which leaves d as the opposite so lets go throught he trig functions.

sin(D) = d/e

cos(D) = f/e

tan(D) = d/f

Now let's do the same with F. d is adjacent, e is the hypotenuse and f is opposite.

sin(F) = f/e

cos(F) = d/e

tam(F) = f/d

Now, you can actually match them up

sin(D) = cos(F)

cos(D) = sin(F)

tan(D) = 1/tan(F) which means tan(F) = 1/tan(D)

And just looking at that we've answered the question. let me know if that doesn't make