Question 443331
Use the sum formula for sine:


*[tex \LARGE \sin{(3x)} = \sin(2x + x) = \sin(2x)\cos(x) + \sin(x)\cos(2x)]


*[tex \LARGE = 2\sin(x)\cos(x)\cos(x) + \sin(x)(\cos^2(x) - \sin^2(x))]


*[tex \LARGE = 2\sin(x)\cos^2(x) + \sin(x)\cos^2(x) - \sin^3(x)]


*[tex \LARGE = 3\sin(x)\cos^2(x) - \sin^3(x)]


Replace cos^2(x) with 1 - sin^2(x):


*[tex \LARGE = 3\sin(x)(1 - \sin^2(x)) - \sin^3(x)]


*[tex \LARGE = 3\sin(x) - 3\sin^3(x) - \sin^3(x)]


*[tex \LARGE = 3\sin(x) - 4\sin^3(x)]


Hence, the statement is an identity.