Express sin 2x cos 4x as a sum of trigonometric functions

Answer 1

From the familiar
sin(A+B)=sin(A)cos(B)+cos(A)sin(B), and
sin(A-B)=sin(A)cos(B)-cos(A)sin(B)
Add both equations to get
sin(A+B)+sin(A-B)=2sin(A)cos(B) .....(3)
But
2x=3x-x
4x=3x+x,
so substitute A=3x, B=x into equation (3) and simplify to get your answer.