# Thread: New problem: 2cos^2 2x = cos2x + 1

1. ## New problem: 2cos^2 2x = cos2x + 1

This time with a harder one. All the hints are really appreciated. Been banging my head to wall few days with this one...

So, here it is:

$2\cos^2 2x = \cos 2x + 1$

Thanks!

--
When you think you know it, you don't!

2. Originally Posted by thex10
This time with a harder one. All the hints are really appreciated. Been banging my head to wall few days with this one...

So, here it is:

$2\cos^2 2x = \cos 2x + 1$

Thanks!

--
When you think you know it, you don't!
Note that you can rewrite it as $2\cos^22x-\cos 2x-1=0$. Also observe that if you make a substitution, say $u=\cos 2x$, the equation becomes quadratic in form: $2u^2-u-1=0$.

Solve this quadratic equation for u, and then backsubstitute $u=\cos 2x$ to find x.

Can you take it from here?

3. Originally Posted by thex10
This time with a harder one. All the hints are really appreciated. Been banging my head to wall few days with this one...

So, here it is:

$2\cos^2 2x = \cos 2x + 1$

Thanks!

--
When you think you know it, you don't!
What are you suppose to be doin? verifying the identity or findin the solutions?

4. Originally Posted by purplec16
What are you suppose to be doin? verifying the identity or findin the solutions?
the equation is conditional ... it's not an identity.

5. Originally Posted by Chris L T521
Note that you can rewrite it as $2\cos^22x-\cos 2x-1=0$. Also observe that if you make a substitution, say $u=\cos 2x$, the equation becomes quadratic in form: $2u^2-u-1=0$.

Solve this quadratic equation for u, and then backsubstitute $u=\cos 2x$ to find x.

Can you take it from here?
Thank you! Now I understood it

--
When you think you know it, you don't!