Proving Product-to-Sum Identities: Need help

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Homework Help Overview

The original poster seeks assistance in proving product-to-sum identities related to trigonometric functions, specifically involving cosine and sine. The identities in question are expressions that relate products of trigonometric functions to sums.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants suggest utilizing known sum and difference formulas for cosine to aid in the proof. Others inquire about the definitions and specifics of these formulas, indicating a need for clarification on foundational concepts.

Discussion Status

The discussion is ongoing, with participants exploring the necessary formulas and definitions. There is an indication that helpful guidance has been offered regarding the use of sum and difference formulas, but no consensus has been reached on the approach to the proofs.

Contextual Notes

The original poster expresses difficulty with proving identities and notes that assistance from teacher assistants is unavailable for this problem set, which may contribute to the urgency of their request for help.

AzureNight
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Homework Statement


Prove the following product-to-sum identities:
i) cosucosv = 1/2[cos(u + v)+cos(u - v)]

ii) sinusinv = 1/2[cos(u - v) - cos(u + v)]

Any help/hints would be appreciated. The TAs (teacher assistants) can't help us with our problem set questions, so I'm stuck on this one. I really suck at proving identities. :(
 
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You must have sum and difference formulas for cos(u+v) and cos(u-v), right? Use them.
 
What do you mean by sum and difference formulas?
 
cos(u+v)=cos(u)cos(v)-sin(u)sin(v). What's cos(u-v)?
 

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