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 ##