Function f ( x) = sin x − cos x is monotonic increasing when

$f '( x) = cos x+\sin x$

$=\sqrt{2}(\frac{1}{\sqrt{2}}\cos x+\frac{1}{\sqrt{2}}\sin x)=\sqrt{2}\sin(\frac{π}{4}+x)$

Now $f(x)$ is monotonic increasing when $f '(x)>0$

$⇒\sqrt{2}\sin(\frac{π}{4}+x)>0$

$⇒0<\frac{π}{4}+x<π$  (∵ $\sin θ$ is positive when $0 < θ <π$)

$∴x∈(\frac{-π}{4},\frac{3π}{4})$