#### Triple angle identity for sines function

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

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

Given sines of a triple angle, there are three solutions for the cubic root of sines of one-third of the triple angle 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.

\sin 3\alpha =3\sin \alpha -4\sin^3\alpha

or