Question

Express the sum or difference as a product. sin 4x - sin 6x
A. 2 cos 4x cos 5x
B. 2 sin 5x cos x
C. -2 sin x cos 5x
D. -2 sin x

Answer 1

you can use the identity

Answer 2

idk how

Answer 3

help please

Answer 4

\[\sin(A)-\sin(B)=2\cos((A+B)/2)) \sin((A-B)/2))\]

Answer 5

i dont get it

Answer 6

@Sila1453

Answer 7

Look on page 2 of this identify reference sheet

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

look at the section called `Sum to Product Formulas`

You'll see this identity

\[\Large \sin(\alpha) - \sin(\beta) = 2*\cos\left(\frac{\alpha+\beta}{2}\right)*\sin\left(\frac{\alpha-\beta}{2}\right)\]


In this case,
alpha = 4x
beta = 6x

Answer 8

im so confused

Answer 9

\(\Large {\color{red}{\alpha}}\) = greek letter alpha = \(\Large {\color{red}{4x}}\)

\(\Large {\color{green}{\beta}}\) = greek letter beta = \(\Large {\color{green}{6x}}\)

-------------------------------------------------

\[\Large \sin(\alpha) - \sin(\beta) = 2*\cos\left(\frac{\alpha+\beta}{2}\right)*\sin\left(\frac{\alpha-\beta}{2}\right)\]

\[\Large \sin({\color{red}{\alpha}}) - \sin({\color{green}{\beta}}) = 2*\cos\left(\frac{{\color{red}{\alpha}}+{\color{green}{\beta}}}{2}\right)*\sin\left(\frac{{\color{red}{\alpha}}-{\color{green}{\beta}}}{2}\right)\]

\[\Large \sin({\color{red}{4x}}) - \sin({\color{green}{6x}}) = 2*\cos\left(\frac{{\color{red}{4x}}+{\color{green}{6x}}}{2}\right)*\sin\left(\frac{{\color{red}{4x}}-{\color{green}{6x}}}{2}\right)\]

Does that help?

Answer 10

no

Answer 11

how does that relate to my question

Answer 12

what would \(\LARGE \frac{4x+6x}{2}\) simplify to?

Answer 13

10x/2

Answer 14

10x/2 can be simplified to what?

Answer 15

20

Answer 16

10 divided by 2 is what?

Answer 17

5

Answer 18

so \(\LARGE \frac{4x+6x}{2}\) would simplify to 5x

what would \(\LARGE \frac{4x-6x}{2}\) simplify to?

Answer 19

forget it. im just gonna take a guess and hope for the best

Answer 20

thanks for trying to help

Answer 21

You are given a difference: sin 4x - sin 6x.
You are asked to rewrite this as a product (that is, involving multiplication).
In your shoes I'd be looking up a table of trig formulas with an eye to finding one that fits this given situation. Jim Thompson found a "sum to product" formula which is perfect for translating the difference sin 4x - sin 6x to a product.

Looking at Jim's formula: You need to identify the values of alpha and beta such that alpha + beta = 4 and alpha - beta = 6. This is a nice algebra problem that is not difficult to solve.

It's about time that you start putting to use the info shared with you by your helpers. So far every response of yours has been negative: No, how does that relate to my question, I'm so confused, and so on. What have you actually done towards solving this problem? Again, you may have to find a list of trig formulas / identities and then search that list for relevant formulas.

Please show some action. Jim has given you plenty of information; it's time that you ask questions if this material is still not clear, or get to work calculating the values of alpha and beta and then re-writing the original expression.

Answer 22

or you can flutter off

Answer 23

Unfortunately, you are not going to get away with such an attitude. I am a Moderator here on OpenStudy, a fact which you apparently ignored or did not recognize. You are not going to speak to me in such a manner.

come back when you're willing to work.

Answer 24

i really dont care