Prove another Trigonometric Function

AI Thread Summary
The discussion revolves around solving a trigonometric function problem, with the original poster expressing frustration over incorrect calculations and a lack of clarity in their curriculum. They initially misapplied the cosine addition identities, which led to confusion in solving the problem. After receiving feedback, they corrected their approach for the first two parts but continued to struggle with the latter parts, particularly in applying the Pythagorean identities. Suggestions were made to substitute only one expression at a time to simplify the problem. The conversation highlights the challenges faced in understanding and applying trigonometric identities effectively.
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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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