Find all values of \(x\) such that \(0\leq x\leq 2\pi\) and \( \sin(x)-\cos(x) = \dfrac{1}{\sqrt{2}}\).
been stuck on this for a while now, help would be appreciated!
$\sin x - \cos x = \frac{1}{\sqrt{2}}$
$1 - \sin 2x = \frac{1}{2}$
$\sin 2x = \frac{1}{2}$
$2x = \frac{\pi}{6}$ or $2x = \frac{5 \pi}{6}$
$x = \frac{\pi}{12}$ or $x = \frac{5 \pi}{12}$
Thanks for answering guest but you need to put your latex in a latex box for it to render properly.
+132 
