Product to Sum Identity

[gnewcom1]

I was wondering if anyone could show how to solve this:
From the product identity cos(x/2)cos(x/4)=1/2[cos(3x/4) + cos(x/4)]
Find the corresponding sum: cos(x/2) cos(x/4) cos(x/8) cos(x/16) = ???

Also what is the product of: cos(x/2) cos(x/4)...............cos(x/2^n) ?

I realize it may have to do something with Viete's formula????

 

[Deleted member 4993]

I was wondering if anyone could show how to solve this:
From the product identity cos(x/2)cos(x/4)=1/2[cos(3x/4) + cos(x/4)]
Find the corresponding sum: cos(x/2) cos(x/4) cos(x/8) cos(x/16) = ???

Also what is the product of: cos(x/2) cos(x/4)...............cos(x/2^n) ?

I realize it may have to do something with Viete's formula????

Please show us your work and tell us exactly where you are stuck:

Hint:

Use

\(\displaystyle Cos(A+B) + Cos(A-B) = 2\cdot CosA \cdot CosB\)

 

[gnewcom1]

I have no idea were to start or what i'm trying to see here. Thats why i asked if anyone knew how to solve it???

 

[Deleted member 4993]

Do you know how to use the equation (formula) I posted above?

If no - what have you been taught in the class?

 

[stapel]

I have no idea were to start or what i'm trying to see here.

A good place to start might be to use the identity that the tutor recommended. :idea:

But if you have "no idea" what you're trying to do (that is, if you don't know what identities are or how one goes about proving them), then I'm afraid you need much more in-depth help than we can here provide. Sorry!

Please consider hiring a qualified local tutor, and setting aside a few hours a week for concentrated face-to-face re-teaching. Good luck!

Eliz.