Question

Prove the identity: cos(3x) + cos(x) = 2cos(2x)cos(x)

I'm almost done with my homework, just got stuck on this one.

Answer 1

`cos \alpha +cos \beta =2\cdot cos ( \alpha + \beta )/(2) \cdot cos ( \alpha - \beta )/(2)\\-----------------\\\\ \alpha =3x\ \ \ and\ \ \ \beta =x\\\\`


`L=cos \alpha +cos \beta =cos(3x)+cos(x)\\\\\Rightarrow\ \ \ 2\cdot cos ( \alpha + \beta )/(2) \cdot cos ( \alpha - \beta )/(2)=2\cdot cos (3x+x)/(2) \cdot cos (3x-x)/(2) =\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos (4x)/(2) \cdot cos (2x)/(2) =\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos(2x)\cdot cos (x)=R`