Expert: Steve Holleran - 7/14/2007

Question
how do you prove the following

tan x + tan y + tan z = (tan x)(tan y)(tan z)

Answer
Hi Brandon,

The problem here is that you don't.

This is not an identity.  Identities have to be true for ALL values, and this particular equation is definitely not true if  x, y , and z are = 45 degrees , or pi/4.

Since tan 45 = 1, if you let x,y and z = 45 you have:

          1 + 1 + 1 = 1 * 1 * 1

                  3 = 1   false.

Therefore, I don't see any way of proving this.

I hope this helps out.

Steve Holleran