This is actually part of a calculus problem, but the part I was struggling with was pure trig, so here you are:

$\displaystyle 2cos^2(2x) - 2sin^2(2x)$

The back of the book simplifies this to:

$\displaystyle 2cos(4x)$

How?

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- Sep 29th 2009, 11:43 AMseuzy13Cosine, sine subtraction problem
This is actually part of a calculus problem, but the part I was struggling with was pure trig, so here you are:

$\displaystyle 2cos^2(2x) - 2sin^2(2x)$

The back of the book simplifies this to:

$\displaystyle 2cos(4x)$

How? - Sep 29th 2009, 11:56 AMAmer
- Sep 29th 2009, 12:03 PMseuzy13
$\displaystyle \cos 2x =\cos ^2 x - \sin ^2 x $

Do you happen to know what the general term for this kind of equation is, so I can look it up in my trig book? The problem is when I went to calculus, I skipped trig, so some of these basic "you should know" things are completely new to me. (Worried)

Also confused about how you did the last line:

$\displaystyle 2( \cos 2(2x)) = 2\cos (4x) $ - Sep 29th 2009, 12:14 PMAmer
there is no general term you should memories formulas

memories the formula in this link not all but the important ones like

$\displaystyle \sin 2x =?? , \cos 2x = ?? , sin^2 x + cos^2 x =?? $

something like that

Math Forum: Ask Dr. Math FAQ: Trigonometry Formulas

the thing that you are confused from it , I just multiply 2(2x) = 4x what hard in this . - Sep 29th 2009, 12:17 PMseuzy13
- Sep 29th 2009, 12:25 PMseuzy13
Never mind. I think I get it now. Thanks a bunch!