Linearización

cosx^5 = (1/2(z+1/z))^5 = (1/32)[z^5 + 5z^3 + 10z + 10z^-1 + 5z^-3 + z^-5] = (1/32)[cos5x+isin5x + 5cos3x+5isin3x + 10cosx+10isinx + 10cosx-10isinx + 5cos3x-5isin3x + cos5x-5isinx]

Saludos.
León-Sotelo.

http://www.math10.com/en/algebra/hyperbolic-functions/hyperbolic-functions.html