The expression 4 sin x cos x is equivalent to which of the following?

Question

(Note: sin (x+y) = sin x cos y + cos x sin y)

F. 2 sin 2x
G. 2 cos 2x
H. 2 sin 4x
J. 8 sin 2x
K. 8 cos 2x

Can someone please explain how to do this problem to me?

Answer 1

Given:
sin(x+y)=sin(x)cos(y) + cos(x)sin(y)

For the case y=x:
sin(x+x) = sin(x)cos(x) + cos(x)sin(x)
=sin(2x) = 2sin(x)cos(x)
or, just to make it easier
2sin(x)cos(x) = sin(2x)
so, what does 4sin(x)cos(x) = ?