How to solve for x

**l flipboi l** · Feb 24th 2010, 02:11 PM

Hello,

How do you solve for x? do you have to factor out cosine? how?

$-2cos(x)-2cos2(x) = 0$

Thanks!

**icemanfan** · Feb 24th 2010, 02:29 PM

$-2 \cos x -2 \cos(2x) = -2 \cos x - 2 (2 \cos^2x - 1) = -4 \cos^2 x - 2 \cos x + 2$ (this identity comes from your other post).

Hence
$-4 \cos^2 x - 2 \cos x + 2 = 0$

$2 \cos^2 x + \cos x - 1 = 0$

Set $z = \cos x$ , then

$2z^2 + z - 1$ .

Solve for z using the quadratic formula

**Grandad** · Feb 25th 2010, 02:53 AM

Hello everyone

Originally Posted by icemanfan

... $2z^2 + z - 1$ .

Solve for z using the quadratic formula

Or, better still, by factorising.

Grandad

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