# Thread: Cosine, sine subtraction problem

1. ## 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:
$\displaystyle 2cos^2(2x) - 2sin^2(2x)$

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

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

The back of the book simplifies this to:
$\displaystyle 2cos(4x)$
How?
you should know that

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

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

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

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

3. Originally Posted by Amer
you should know that

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

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

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

$\displaystyle 2( \cos 2(2x)) = 2\cos (4x)$
$\displaystyle \cos 2x =\cos ^2 x - \sin ^2 x$
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.
Also confused about how you did the last line:
$\displaystyle 2( \cos 2(2x)) = 2\cos (4x)$

4. Originally Posted by seuzy13
$\displaystyle \cos 2x =\cos ^2 x - \sin ^2 x$
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.
Also confused about how you did the last line:
$\displaystyle 2( \cos 2(2x)) = 2\cos (4x)$
there is no general term you should memories formulas

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

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

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 .

5. 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

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

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 .
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.

6. Never mind. I think I get it now. Thanks a bunch!