# How do you solve cosx=3cosx-2?

Aug 28, 2016

$x = 0 \mathmr{and} 2 \pi$

#### Explanation:

If we let $\cos x = w$, then we can simplify our equation:

$\cos x = 3 \cos x - 2$
$w = 3 w - 2$

Next, isolate the $w$ terms to one side:

$w - w + 2 = 3 w - 2 - w + 2$
$2 = 3 w - w$
$2 = 2 w$
$w = 1$

Replace $w$ with $\cos x$:

$w = 1$
$\cos x = 1$
$x = {\cos}^{-} 1 \left(1\right)$
$x = 0 \mathmr{and} 2 \pi$

Note: Technically, since the $\cos x$ function completes a full cycle for every $2 \pi$ radians, $x$ could be more accurately defined as:

$x = 2 \pi n$ where $n \in \mathbb{Z}$