Mastering Trigonometric Equations: Solving cos 2x-cos^2 x=0

[lep11]

Homework Statement

cos 2x-cos^2 x=0

The Attempt at a Solution

I have no idea.

 

[BloodyFrozen]

Try getting everything in terms of $cos^{2}{x}$

What is $cos(2x)$ equaled to? Hint. Double angle identity.

 

[lep11]

Try getting everything in terms of $cos^{2}{x}$

What is $cos(2x)$ equaled to? Hint. Double angle identity.

cos2x=2cos^2 -1
Therefore 2cos^2 x -1 -cos^2 x=0
How to continue?

 

[BloodyFrozen]

cos2x=2cos^2 -1
Therefore 2cos^2 x -1 -cos^2 x=0
How to continue?

Don't substitute it in yet.

$cos(2x)$ has multiple identities; it also equals:

$$cos(2x) = cos^{2}(x) - sin^{2} (x)$$

How can you change the $sin^{2} (x)$ into cosines?

 

[lep11]

Anyone?

 

[I like Serena]

You already had 2cos^2 x -1 -cos^2 x=0.

Can you replace each occurrence of (cos^2 x) by y?
And then solve for y?