# Homework Help: Trig identity proof

1. Jul 13, 2012

### Aaron H.

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

Prove the identity.

2. Relevant equations

http://postimage.org/image/vjhwki1ax/ [Broken]

3. The attempt at a solution

http://s13.postimage.org/jkhubi4lz/DSC03534.jpg

Last edited by a moderator: May 6, 2017
2. Jul 13, 2012

### Staff: Mentor

Speaking only for myself, I would be more inclined to help out if I didn't have to open one link to see the problem, and open another link to see what you did.

3. Jul 13, 2012

### Villyer

I noticed that after all of your work, you got the problem to cos(3x)cos(x)-sin(x)sin(3x).

Using sec(x) = 1/cos(x) and csc(x) = 1/sin(x);

cos(3x)/sec(x) - sin(x)/csc(3x)
cos(3x)/(1/cos(x)) - sin(x)/(1/sin(3x))
cos(3x)cos(x) - six(x)sin(3x)

4. Jul 13, 2012

### Curious3141

I can't view his solution. But if he's already got it into that form, he can just use the angle sum formula for cosine to express that as $\cos kx$, where k is some positive integer (which he needs to work out). Then use the double angle formula for cosine to split it up again, yielding the required proof.

5. Jul 13, 2012

### eumyang

Looking at the OP's solution, the OP went the complicated route to go from the LHS to the bolded part above. Villyer just simplified the process.

6. Jul 13, 2012

### Aaron H.

cos(3x)cos(x) - six(x)sin(3x)

cos (4x)

cos^2 2x - sin^2 2x

Thanks all.

7. Jul 13, 2012

### Curious3141

Looks great, but you might want to put "=" signs in between the lines.