A variable belongs to some interval

Hi all,

If I ask Maxima to compute cos(2*acos(.8)) or cos(3*acos(-.5)), I get 
the right answers. However, Maxima seems unable to simplify the 
expressions cos(2*acos(x)) or cos(3*acos(x)), even if I use the trigsimp 
command. I would like to declare that _x_ belongs to [-1,1], to see if 
that solves the problem. Is it possible? If not, is there some way of 
making Maxima "see" that

    cos(3*acos(x)) = 4x^3 - 3x?

Best regards,

Jose Carlos Santos