nah, it is stated there to prove the identities/equations.
I have proved it actually but then I've realized that I was wrong and then I couldn't get the process anymore.
cos A + cos 2A + cos 3A = cos 2A(1-cos A)
What I did was to factor cos A, thus it makes cos A (1 + cos A + cos 2A)
then I've realized that it is wrong. Though I aririved at cos 2A(1-cos A)
reiward, Mr Fantastic is correct. What you have is a trigonometric equation, not an identity. His counter-example was when A = 0, that will give you 3 = 0, which is wrong. So it merits to be an equation, not an identity as what you claimed it to be. Se my graph . . . .