# Cosine, sine subtraction problem

• September 29th 2009, 11:43 AM
seuzy13
Cosine, 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:
$2cos^2(2x) - 2sin^2(2x)$

The back of the book simplifies this to:
$2cos(4x)$
How?
• September 29th 2009, 11:56 AM
Amer
Quote:

Originally Posted by seuzy13
This is actually part of a calculus problem, but the part I was struggling with was pure trig, so here you are:
$2cos^2(2x) - 2sin^2(2x)$

The back of the book simplifies this to:
$2cos(4x)$
How?

you should know that

$\cos 2x =\cos ^2 x - \sin ^2 x$ ok so

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

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

$2( \cos 2(2x)) = 2\cos (4x)$
• September 29th 2009, 12:03 PM
seuzy13
Quote:

Originally Posted by Amer
you should know that

$\cos 2x =\cos ^2 x - \sin ^2 x$ ok so

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

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

$2( \cos 2(2x)) = 2\cos (4x)$

$\cos 2x =\cos ^2 x - \sin ^2 x$
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:
$2( \cos 2(2x)) = 2\cos (4x)$
• September 29th 2009, 12:14 PM
Amer
Quote:

Originally Posted by seuzy13
$\cos 2x =\cos ^2 x - \sin ^2 x$
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:
$2( \cos 2(2x)) = 2\cos (4x)$

there is no general term you should memories formulas

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

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

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 .
• September 29th 2009, 12:17 PM
seuzy13
Quote:

Originally Posted by Amer
there is no general term you should memories formulas

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

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

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 .

Confused about why you are multiplying 2(2x) I guess. How you got from second to last step to the last step. Nothing hard about the actual multiplication. Haha. :)
• September 29th 2009, 12:25 PM
seuzy13
Never mind. I think I get it now. Thanks a bunch!