What is the solution to the equation tan²x + cos2x = 1 - cos2xtan²x?

[synergix]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I have not really gotten anywhere.

 

[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.

 

[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

 

[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.

 

[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

 

[synergix]

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

 

[Dick]

Just keep going. Multiply out the terms with parentheses.