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# Trig identity help watch

1. I'm trying to integrate (cos x)(cos 3x).

As below, my teacher has used the compound angle formulas. What I don't understand is, he has interchanged the A and B on each formula. For cos(A+B) he has done cos(x+3x), but for cos(A-B) he's done cos(3x-x). Shouldn't it be cos(x-3x)?

2. (Original post by xtal33)
I'm trying to integrate (cos x)(cos 3x).

As below, my teacher has used the compound angle formulas. What I don't understand is, he has interchanged the A and B on each formula. For cos(A+B) he has done cos(x+3x), but for cos(A-B) he's done cos(3x-x). Shouldn't it be cos(x-3x)?

He's been inconsistent with the order in which the A and B are written in relation to the cos(3x) and cos(x), but it doesn't matter.
Especially since
Spoiler:
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3. If you expand cos(x-3x) and cos(3x-x), you will notice they are identical, this is because cos(x) = cos(-x), so it doesn't matter which way you express them, I assume he's done it just to make it a bit easier

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4. (Original post by JamesDL4)
If you expand cos(x-3x) and cos(3x-x), you will notice they are identical, this is because cos(x) = cos(-x), so it doesn't matter which way you express them, I assume he's done it just to make it a bit easier

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Thanks very much for the replies.

So is it always the case that cos(x) and cos(-x) are identical, no matter what coefficient is in front of the x?

edit; I think I understand now, because the cos graph is identical on either side of the y axis?
5. (Original post by xtal33)
Thanks very much for the replies.

So is it always the case that cos(x) and cos(-x) are identical, no matter what coefficient is in front of the x?
If by coefficient in front you mean cos(nx) = cos(-nx) then yes
EDIT: And yes to your edit.
6. (Original post by joostan)
If by coefficient in front you mean cos(nx) = cos(-nx) then yes
EDIT: And yes to your edit.
Would sin(x) and sin(-x) be identical? I'm guessing not but I'm not sure.
7. (Original post by xtal33)
Would sin(x) and sin(-x) be identical? I'm guessing not but I'm not sure.
Try a value on your calculator to see?
8. (Original post by Mr M)
Try a value on your calculator to see?
Ah right, they're not. Thanks again.
9. (Original post by xtal33)
Ah right, they're not. Thanks again.
Did you spot a different relationship between them while you were at it?

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