Thread: How to solve for x

Hello,

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

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


Thanks!

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

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

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

Set $\displaystyle z = \cos x$, then

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

Solve for z using the quadratic formula

Hello everyone

Originally Posted by icemanfan

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

Solve for z using the quadratic formula

Or, better still, by factorising.

Grandad