trig

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

(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?

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  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) = ?

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