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

$x∈(0,\frac{π}{2})$ $x∈(\frac{-π}{4},\frac{π}{4})$ $x∈(\frac{-π}{4},\frac{3π}{4})$ No where

$x∈(\frac{-π}{4},\frac{3π}{4})$

$f '( x) = cos x+\sin x$ $=\sqrt{2}(\frac{1}{\sqrt{2}}\cos x+\frac{1}{\sqrt{2}}\sin x)=\sqrt{2}\sin(\frac{π}{4}+x)$ 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 $0 < θ <π$) $∴x∈(\frac{-π}{4},\frac{3π}{4})$