#### Triple angle identity for cosine function

Triple angle identity for cosine function is used to represent cosine of a triple angle in terms of cosine of one-third of the triple angle. More specifically, cosine of a triple angle equals to the difference between 4 multiples of cosine of one-third of the triple angle to power three and three multiples of cosine of one-third of the triple angle.

Triple angle identity for cosine function is often used to simplify trigonometric expressions or solve specific cubic equations.

If taking cosine of one-third of the triple angle as a variable, given cosine of a triple angle, there are three solutions according to de Moivre’s formula. It is also true to find solutions for the cubic equations that are alike to the triple root identity.

\cos 3\alpha =4\cos^3\alpha -3\cos \alpha

or