Question

How can this be solved?

`(sin^4x - 2sin^2x + 1)cosx = cos^5x`

Answer 1

I don't know. Can it?

Explanation:

Problems like this are typically testing you how well you are able to operate on equations. Sometimes you need to try a number of paths but be confident in your toolkit. You want to search for identities that you have in class to see if there are ways to move forward (simplify). Sometimes it cannot be simplified, but try a few methods first.

`(sin^4x - 2sin^2x + 1)cosx = cos^5x`

Right off the bat it looks like you can devide both sides by `cos(x)`.

`sin^4x - 2sin^2x + 1 = cos^4x`

Problems with a conspicuous looking `1` often acquire the following identity `1 = sin^2x cos^2x`.

`sin^4x - 2sin^2x + sin^2x + cos^2x = cos^4x`

`sin^4x - sin^2x + cos^2x = cos^4x`

That's as far as I can meaningfully go. See if you can use any identities from here.