$\sin x+\cos x$ (*)
Ta biết $\sin\dfrac{\pi}{4}=\cos\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}$
nên khi chia (*) cho $\sqrt2$ rồi lại nhân $\sqrt2$, ta có:
$\sqrt2(\dfrac{1}{\sqrt2}.\sin x+\dfrac{1}{\sqrt2}\cos x)$
$=\sqrt2(\cos\dfrac{\pi}{4}.\sin x+\cos x.\sin\dfrac{\pi}{4})$
$=\sqrt2\sin(x+\dfrac{\pi}{4})$ (theo CT cộng)