Prove another Trigonometric Function

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Homework Help Overview

The discussion revolves around proving trigonometric identities, specifically involving cosine functions and their relationships with sine functions. Participants are attempting to navigate through various trigonometric identities and their applications in solving the problem presented.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing the correct application of cosine addition identities and the First Pythagorean Identity. There are attempts to expand and manipulate trigonometric expressions, with some participants expressing confusion over their calculations and the curriculum's explanations.

Discussion Status

Some participants have identified errors in their initial approaches and are seeking clarification on how to correctly apply trigonometric identities. There is ongoing exploration of different methods to simplify or transform the equations, with no clear consensus on the next steps yet.

Contextual Notes

Participants mention difficulties with the curriculum's explanations and express uncertainty about applying identities when variables are multiplied by constants. There is a sense of frustration regarding the clarity of the material provided in their studies.

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Homework Statement



http://img362.imageshack.us/img362/1465/problemcn2.jpg
http://g.imageshack.us/g.php?h=362&i=problemcn2.jpg

Homework Equations


http://img510.imageshack.us/img510/3137/formula1df4.jpg
http://g.imageshack.us/g.php?h=510&i=formula1df4.jpg

http://img411.imageshack.us/img411/7889/formula2mn1.jpg
http://g.imageshack.us/g.php?h=411&i=formula2mn1.jpg


The Attempt at a Solution



http://img380.imageshack.us/img380/5177/attemptsu1.jpg
http://g.imageshack.us/g.php?h=380&i=attemptsu1.jpg

As you can see, none of my calculations match. Please help anyone. I know this is very difficult to explain but I'm all ears. This question's been bothering me all afternoon. The curriculum does not explain it well. At all.

Mega thanks in advance.
 
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You got the formulas for cos(X+B) and cos(X-B) wrong.
 
Oh, damn am I stupid. Thanks for telling me about the mistake.

Alright guys, I got the first 2 parts correct so far (because of the correct Cos addition identity). Now on to the next two. I'm not out of the woods yet.
 
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Look at your list of trig identities. Which ones involve cos^2 and/or sin^2?
 
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Ok, so you know 1. \sin^2 \theta = 1 - \cos^2 \theta 2. \cos^2 \theta = 1 - \sin^2 \theta. With your cos^2 - sin^2 form, replace the appropriate terms.
 
Ok. I tried doing that but it just brought me back to the original equation.

http://img244.imageshack.us/img244/7475/pict0139ko2.jpg
http://g.imageshack.us/g.php?h=244&i=pict0139ko2.jpg

As well, I don't know how to apply the First Pythagorean Identity to sin or cos if it is multiplied by 2. It changes things. And they never went over how to mechanically solve these operations in my curriculum.
 
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