# Math Help - Equation help

1. ## Equation help

Hello i have problems solving this one

x= π/4 + k π/2

thanks

2. note that $\displaystyle \sin^2{u} = \frac{1 - \cos(2u)}{2}$

$\displaystyle \frac{1 - \cos{x}}{1 - \cos{2x}} = 1 - \cos{x}
$

since $\sin{x} \ne 0$ , $\cos{x} \ne 1$ ...

$\displaystyle \frac{1}{1 - \cos(2x)} = 1$

$\cos(2x) = 0$

$\displaystyle 2x = \frac{\pi}{2} + k\pi \, ; \, k \in \mathbb{Z}$

$\displaystyle x = \frac{\pi}{4} + \frac{k\pi}{2}$

3. Hi i understand but at the end why

and not
2x= π/2 + 2 k π

i can't understand that part ...
thank you

4. Originally Posted by pauline
Hi i understand but at the end why

and not
2x= π/2 + 2 k π

i can't understand that part ...
thank you
because $\cos{u} = 0$ at $\displaystyle u = \pm \frac{\pi}{2} \, , \, \pm \frac{3\pi}{2} \, , \, \pm \frac{5\pi}{2} \, , \, ...$