Simplify the trigonometric expression sin (4x) + 2 sin (2x) using Double-Angle

Identities.

8sin (x) cos³ (x)

Step-by-step explanation:

sin (4x) + 2 sin (2x) = 2sin (2x) * cos (2x) + 2sin (2x) = 2sin (2x) (cos2x + 1) =

= 2sin (2x) (cos²x - sin²x + cos²x + sin²x) = ²2sin (2x) * (2cos²x) =

= 4*2sin (x) * cos (x) * cos² (x) = 8sin (x) cos³ (x)