Question

determinati x apartine (0,pi) stiind ca sin x-cos x=radical 2

Answer 1

Răspuns:

$\boxed{x=\frac{3\pi}{4} }$

Explicație pas cu pas:

$sin(x)-cos(x)=\sqrt2\\sin^2x-2sin(x)cos(x)+cos^2x=2\\sin^2x+cos^2x-sin(2x)=2\\sin(2x)=-1$

$2x=\frac{3\pi}{2} +2k\pi\\x=\frac{3\pi}{4} +k\pi$

$0 < \frac{3\pi}{4} +k\pi < \pi\\\frac{-3\pi}{4} < k\pi < \frac{\pi}{4} \\\frac{-3}{4} < k < \frac{1}{4} \\k \in \mathbb{Z} \implies k=0$