Question

sin(x)/(2)-cos(x)/(2)=0

Answer 1

$\frac {sin(x)}{2} - \frac {cos(x)}{2}=0$

$\frac {1}{2} (sin(x) - cos(x))=0$

$-\frac {sin(\frac{\pi}{4}-x)}{\sqrt{2}}=0$

$x=\pi n - \frac {3\pi}{4}$, n ∈ Ƶ

Answer 2

Ответ:

$\dfrac{\pi}{2}+2\pi n, \quad n \in \mathbb {Z};$

Объяснение:

$sin\dfrac{x}{2}-cos\dfrac{x}{2}=0 \quad \bigg | \quad :cos\dfrac{x}{2} \neq 0;$

$tg\dfrac{x}{2}-1=0;$

$tg\dfrac{x}{2}=1;$

$\dfrac{x}{2}=arctg(1)+\pi n, \quad n \in \mathbb {Z};$

$\dfrac{x}{2}=\dfrac{\pi}{4}+\pi n, \quad n \in \mathbb {Z};$

$x=\dfrac{\pi}{2}+2\pi n, \quad n \in \mathbb {Z};$

$n=0: \quad \dfrac{x}{2}=\dfrac{\pi}{4}; \quad cos\dfrac{\pi}{4}=\dfrac{\sqrt{2}}{2} \neq 0;$