Решите уравнения: 1) tg(x-3pi/4)+1=0 2) ctg(3,5pi+x)=0 3) 3sinx-8=sqrt2

$1) \ tg \bigg(x - \dfrac{3\pi}{4} \bigg) + 1 = 0$

$tg \bigg(x - \dfrac{3\pi}{4} \bigg) = -1$

$x - \dfrac{3\pi}{4} = arctg(-1)$

$x - \dfrac{3\pi}{4} = -\dfrac{\pi}{4}$

$x - \dfrac{3\pi}{4} = -\dfrac{\pi}{4} + \pi n, n \in Z$

$x = -\dfrac{\pi}{4} + \dfrac{3\pi}{4} + \pi n, n \in Z$

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

$2) \ ctg (3,5 \pi + x) = 0$

$-tg \ x = 0$

$tg \ x = 0$

$x = \pi n, n \in Z$

$3) \ 3sin \ x - 8 = \sqrt{2}$

ОДЗ: $x \in [-1; 1]$

$3sin \ x = \sqrt{2} + 8$

$sin \ x \approx \dfrac{1,41 + 8}{3} = \dfrac{9,41}{3} \approx 3,14$

$\oslash$ (Нет решений).