# Thread: (cosx^2)/x=cosx true or false. Explain.

1. ## (cosx^2)/x=cosx true or false. Explain.

For all real values of X.

Is the following true or false? Provide reasoning for your answers.

(cosx^2)/x=cosx

I know it is false. Cos cannot be factored out of an expression.

I just have a hard time coming up with the right words or proof why this is the case.

2. ## Re: (cosx^2)/x=cosx true or false. Explain.

Originally Posted by StudentMCCS
For all real values of X.

Is the following true or false? Provide reasoning for your answers.

(cosx^2)/x=cosx

I know it is false. Cos cannot be factored out of an expression.

I just have a hard time coming up with the right words or proof why this is the case.
it's not an identity, but is a valid conditional equation ...

$\displaystyle \frac{\cos^2{x}}{x} = \cos{x}$

$\displaystyle \frac{\cos^2{x}}{x} - \cos{x} = 0$

$\displaystyle \cos{x}\left(\frac{\cos{x}}{x} - 1\right) = 0$

$\displaystyle \cos{x} = 0$ ... lots of solutions

$\displaystyle \cos{x} = x$ ... one solution