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

  • maths -

    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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