Đáp án:
$x = -\dfrac{ \pi}4 + k \pi$ $(k\in\mathbb Z)$
Lời giải:
$\sin x+\cos x=0$
$\Leftrightarrow\sqrt2\left({\dfrac1{\sqrt2}\sin x+\dfrac1{\sqrt2}\cos x}\right)=0$
$\Leftrightarrow\sqrt2\left({\cos\dfrac{\pi}4\sin x+\sin\dfrac{\pi}4\cos x}\right)=0$
$\Leftrightarrow\sqrt2 \sin\left({x+ \dfrac{\pi}4}\right) = 0$
$⇔ \sin\left({x+\dfrac{\pi}4}\right) = 0$
$⇔ x + \dfrac{\pi}4 = k\pi$
$⇔ x = -\dfrac{ \pi}4 + k \pi$ $(k\in\mathbb Z)$.
