How do you solve $cos x = 3 cos x - 2$ $cosx=3cosx-2$ ?

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How do you solve $cos x = 3 cos x - 2$ $cosx=3cosx-2$ ?

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Answer 1 · 2016-08-28T04:16:11

$x = 0 or 2 π$ $x=0 or 2 pi$

Explanation:

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

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

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

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

Replace $w$ $w$ with $cos x$ $cosx$ :

$w = 1$ $w=1$
$cos x = 1$ $cosx=1$
$x = {cos}^{- 1} (1)$ $x=cos^-1(1)$
$x = 0 or 2 π$ $x=0 or 2pi$

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

$x = 2 π n$ $x=2pin$ where $ninZZ$

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How do you solve $cos x = 3 cos x - 2$ $cosx=3cosx-2$ ?

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