hey guys having trouble simplying this expression. Any help? thank u

$\displaystyle

2sin3xcos3xcos5x-(cos^23x-sin^23x)sin5x

$

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- Sep 9th 2008, 07:33 AMjvignacioSimplifying the expression
hey guys having trouble simplying this expression. Any help? thank u

$\displaystyle

2sin3xcos3xcos5x-(cos^23x-sin^23x)sin5x

$ - Sep 9th 2008, 08:03 AMKrizalid
Use the double angle formulae for sin and cosine.

(Sorry for my poor help but I'm in a rush.) - Sep 9th 2008, 08:08 AMChop Suey
Just to add more:

$\displaystyle \cos{2x} = \cos^2{x} - \sin^2{x}$

$\displaystyle \cos{4x} = \cos^2{2x} - \sin^2{2x}$

$\displaystyle \ldots$

==================

$\displaystyle \sin{2x} = 2\sin{x}\cos{x}$

$\displaystyle \sin{4x} = 2\sin{2x}\cos{2x}$

$\displaystyle \ldots$

Do you see the pattern here? - Sep 9th 2008, 08:19 AMjvignacio
- Sep 9th 2008, 08:34 AMjvignacio
- Sep 9th 2008, 08:40 AMChop Suey
You only needed to change the 2sin3xcos3x and (cos^2(3x) - sin^2(3x)).

Then, you'll see that this fits the sum identitiy for sine. Recall that:

$\displaystyle \sin{(A+B)} = \sin{A}\cos{B} + \cos{A}\sin{B}$ - Sep 9th 2008, 08:43 AMjvignacio
- Sep 9th 2008, 08:45 AMChop Suey
- Sep 9th 2008, 08:58 AMjvignacio