Posted by tom on Monday, December 24, 2012 at 8:00am.
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.
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