# Prove Identity

1. Feb 13, 2009

### synergix

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

tan^2x + cos2x =1 - cos2xtan^2x

2. Relevant equations

3. The attempt at a solution
I have not really gotten anywhere.

2. Feb 13, 2009

### Dick

Use cos(2x)=cos(x)^2-sin(x)^2 and tan(x)=sin(x)/cos(x) to turn everything into sines and cosines. Then clear out the denominators and start rearranging things.

3. Feb 13, 2009

### synergix

I have gotten it to

(sin(x)^2/cos(x)^2) + (cos(x)^2- sin(x)^2) = 1- (cos (x)^2 - sin(x)^2)(sin(x)^2/cos(x)^2)

not sure how to proceed

4. Feb 13, 2009

### Dick

Good so far. Multiply out the right side and multiply both sides by cos(x)^2 to clear out the fractions. Does anything cancel? Rearrange what's left.

5. Feb 13, 2009

### synergix

Its just not happenin for me right now

I have it at sin(x)^2 cos(x)^2(cos(x)^2 - sin(x)^2) = cos(x)^2 - (cos(x)^2- sin(x)^2) sin(x)^2

6. Feb 13, 2009

### synergix

I meant to put a + after the first sin(x)^2

7. Feb 13, 2009

### Dick

Just keep going. Multiply out the terms with parentheses.