Prove another Trigonometric Function

[Sabellic]

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.

 

[ahmadmz]

You got the formulas for cos(X+B) and cos(X-B) wrong.

 

[Gib Z]

http://www.mathwords.com/s/sum_difference_identities.htm

Expand the cos 2theta form correctly, then form 2 has no need to be proven, and 3 & 4 come from Pythagorean identities.

 

[Sabellic]

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.

 

[Sabellic]

I'm still having troubles with the last two. I am trying. Please help me if you can.

http://img377.imageshack.us/img377/792/strugglingiq1.jpg
http://g.imageshack.us/g.php?h=377&i=strugglingiq1.jpg

 

[Redbelly98]

Look at your list of trig identities. Which ones involve cos^2 and/or sin^2?

 

[Sabellic]

The First Pythagorean Identities involve cos^2x and sin^2x

But I am still not getting the correct answer.

http://img240.imageshack.us/img240/6290/pict0138rx6.jpg
http://g.imageshack.us/g.php?h=240&i=pict0138rx6.jpg

 

[Gib Z]

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.

 

[Sabellic]

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.

 

[Sabellic]

Okay, I'm trying a direct replacement for the 3 and 4 Parts:

http://img233.imageshack.us/img233/9161/pict0140hv8.jpg
http://g.imageshack.us/g.php?h=233&i=pict0140hv8.jpg

 

[Redbelly98]

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

Try subbing just one of the expressions, not both.