Triangle ABC is such that AC=BC and AB/BC = r
Show that cos A + cos B + cos C = 1 + r -(r^2/2)
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
Hello, Ph4m
I'll finish what ThePerfectHacker started . . .
We have isosceles triangle ABC with and
Then the triangle looks like this:The sides are: .Code:C * / \ / \ a/ \a / \ / \ A * - - - - - * B ar
From the Law of Cosines, we have:
. .
. .
. .
Therefore: .