help..

tan(A-B)+tan(B-C)+tan(C-A)=tan(A-B)tan(B-C)tan(C-A)

:o :o

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- June 3rd 2006, 12:59 AMJoyce
help..

tan(A-B)+tan(B-C)+tan(C-A)=tan(A-B)tan(B-C)tan(C-A)

:o :o - June 3rd 2006, 01:08 AMmalaygoelQuote:

Originally Posted by**Joyce**

expand it and you will get the answer

:) - June 3rd 2006, 01:25 AMCaptainBlackQuote:

Originally Posted by**Joyce**

Also don't post the same question twice.

RonL - June 3rd 2006, 03:17 AMSoroban
Hello, Joyce!

Quote:

We see that:

So we have:

Take the tangent of both sides:

. . and we have:

Then:

. . Hence:

Therefore:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

How did I come up with this proof?

I saw that this problem was similar to another (classic) problem:

. . If , then:

And the proof is almost identical.