Prove another Trigonometric Function

1. Aug 16, 2008

Sabellic

1. The problem statement, all variables and given/known data

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

2. Relevant equations
http://img510.imageshack.us/img510/3137/formula1df4.jpg [Broken]
http://g.imageshack.us/g.php?h=510&i=formula1df4.jpg [Broken]

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

3. The attempt at a solution

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

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.

Last edited by a moderator: May 3, 2017
2. Aug 16, 2008

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

3. Aug 16, 2008

Gib Z

4. Aug 16, 2008

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.

5. Aug 16, 2008

Sabellic

Last edited by a moderator: May 3, 2017
6. Aug 16, 2008

Redbelly98

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

7. Aug 16, 2008

Sabellic

Last edited by a moderator: May 3, 2017
8. Aug 16, 2008

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.

9. Aug 16, 2008

Sabellic

Ok. I tried doing that but it just brought me back to the original equation.

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

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.

Last edited by a moderator: May 3, 2017
10. Aug 16, 2008

Sabellic

Last edited by a moderator: May 3, 2017
11. Aug 17, 2008

Redbelly98

Staff Emeritus
Last edited by a moderator: May 3, 2017