How do you prove that? Sin4x=4 cos2x sinx cosx
Use algebra and trigonometric identities to change only one side of the equation, until it looks the same as the other side.
I will only change the left side:
Use the identity
Combine the two terms on the left:
Use the identity sin(2x) = 2sin(x)cos(x) on the left:
Multiply the 2s on the left:
The left side looks the same as the right side. Q.E.D.