Question

Can someone proove it to me thank you for your help

Answer 1

$\sin(2x + x) = \sin(2x) \cos(x) + \\ \cos(2x) \sin(x) = 2 \sin(x) { \cos(x) }^{2} \\ + \sin(x) { \cos(x) }^{2} - { \sin(x) }^{3} = \\ 3 \sin(x) { \cos(x) }^{2} - { \sin(x) }^{3} = \\ 3 \sin(x) - 3 { \sin(x) }^{3} - { \sin(x) }^{3} = \\ 3 \sin(x) - 4 { \sin(x) }^{3}$