They want you to make use of this limit identity:
[tex]\rm \lim\limits_{t\to0}\dfrac{sin(t)}{t}=1[/tex]
y=sin(x) and y=x approach zero at the same rate.
So with your problem you simply apply your Sine Double Angle Identity,
[tex]\rm \lim\limits_{x\to0}\dfrac{2sin x cos x}{2x}=\lim\limits_{x\to0}\dfrac{sin(2x)}{2x}[/tex]
From this point, hopefully you can see that we have our identity with t=2x. So yes, you are correct :) the result is 1.
