My proof is a bit long winded. i'm sure someone else will come up with a better one soon.

See the diagram below:

what was described was an isoseles triangle, so we can further assume that:

(1) AD = BD

(2)

Now from the triangle, we see that:

also,

also,

Further more, you should know the identity,

Now to start peicing this together:

Since ,

Also, since ,

and now we're done. just to say what we have to say:

as desired