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## Sunday, November 30, 2008

### A trigonometric identity

$\tan(a)+\tan(b)+\tan(c)= \tan(a)*\tan(b)*\tan(c)&space;\\&space;(&space;a+b+c=180^{\circ}&space;)$

Isn't that beautiful? ( Can you prove it? )

1. You're right. That is beautiful. I'd never seen that before.

You inspired me to write a post this afternoon about the converse to that identity.

2. ummm ... a, b, and c are the angles of a single triangle.

i learned this here.

3. oh. heck. there it is
a + b + c = 180^\circ.

so my attempt at a correction
was misguided. i really *did*
learn this at polymath, though ...

4. Start off with tan(a+b)=tan(\pi-c)=-tan(c). Then expand tan(a+b) using the additive identity. It follows easily from there.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)