$\displaystyle \lim_{x \to \frac{\pi}{4}} \frac{\sin x - \cos x}{x - \frac{\pi}{4}}$ is equal to …
🎥 Video solution / Text Solution of this question is given below:
his is the derivative of $\sin x-\cos x$ at $x=\frac{\pi}{4}$.
$\,(\sin x-\cos x)'=\cos x+\sin x \Rightarrow \cos\frac{\pi}{4}+\sin\frac{\pi}{4}
=\tfrac{\sqrt2}{2}+\tfrac{\sqrt2}{2}=\sqrt2.$