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

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

- maths -
**MathMate**, Monday, December 24, 2012 at 10:03am
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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