Answer
$x=\frac{\pi}{4}$ or $x=\frac{7\pi}{4}$
Work Step by Step
$sin(x+\frac{\pi}{4})-sin(x-\frac{\pi}{4})=1$
$sin~x~cos\frac{\pi}{4}+cos~x~sin\frac{\pi}{4}-(sin~x~cos\frac{\pi}{4}-cos~x~sin\frac{\pi}{4})=1$
$2~cos~x~sin\frac{\pi}{4}=1$
$2~cos~x~\frac{\sqrt 2}{2}=1$
$cos~x=\frac{1}{\sqrt 2}=\frac{\sqrt 2}{2}$
$x=\frac{\pi}{4}$ or $x=\frac{7\pi}{4}$
