How can you simplify sin(2x)cos(2x)?

This is just a trig question to get the solution into a different form;
Recall the sine addition formula:
## sin (A+ B) =sinAcosB + cosAsinB ##
Put ## A=B ## to get a double angle formula;
## sin (A+ A) =sinAcosA + cosAsinA ##
## :. sin (2A) =2sinAcosA ##
If we put ##A=2x## then;
## :. sin (2(2x)) =2sin2xcos2x ##
## :. sin 4x =2sin2xcos2x ##
Hence ## sin2xcos2x = 1/2sin 4x ##