Write as a product of two trig functions. cos2x - cos4x?

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Write as a product of two trig functions. cos2x - cos4x?

2006-12-19 05:58:51 · 3 answers · asked by wicked 1 in Science & Mathematics ➔ Mathematics

3 answers

cosA - cosB = 2 sin½(B+A)sin½(B- A)

So cos2x - cos4x = 2 sin½(4x + 2x)sin½(4x - 2x)

= 2sin3xsinx

2006-12-19 06:10:39 · answer #1 · answered by Wal C 6 · 0⤊ 0⤋

cos2x - cos 4x =
= (cosÂ²x - sinÂ²x ) - (cosÂ²2x - sinÂ²2x) =
= cosÂ²x - sinÂ²x - cosÂ²2x + sinÂ²2x =
= cosÂ²x - sinÂ²x - (cosÂ²x-sinÂ²x)Â² + (2sinxcosx)Â² =

Developing and then simplifying we get:

6cosÂ²xsinÂ²x

That's it!

Good luck!

2006-12-19 14:19:30 · answer #2 · answered by CHESSLARUS 7 · 0⤊ 0⤋

cos(a) - cos(b) = -2sin{(a+b)/2}sin{(a-b)/2}

final answer is

-2sin(3x)sin(-x)

2006-12-19 14:11:42 · answer #3 · answered by rod_dollente 5 · 0⤊ 0⤋