Question

Rezolvati in R ecuatia:

Multumesc!!!!!!

Answer 1

$\mathrm{4\sin x+tg\, x = \sqrt 3 \Big|\cdot \dfrac{\cos x}{2} }\\ \\\mathrm{ 2\sin x\cos x+\dfrac{1}{2}\sin x = \dfrac{\sqrt 3}{2}\cos x} \\ \\ \mathrm{\sin (2x) = \dfrac{\sqrt 3}{2}\cos x} - \dfrac{1}{2}\sin x}\\ \\ \mathrm{\sin(2x) = \sin\Big(\dfrac{\pi}{3}-x\Big)} \\ \\ \mathrm{\Rightarrow 2x = \dfrac{\pi}{3}-x+2k\pi \quad sau\quad 2x = \pi - \Big(\dfrac{\pi}{3}-x\Big)+2k\pi} \\ \\ \mathrm{\Rightarrow x = \dfrac{\pi}{9}+\dfrac{2k\pi}{3}\quad sau\quad x = \dfrac{2\pi}{3}+2k\pi}$

$\mathrm{\Rightarrow x \in \left\{\dfrac{\pi}{9}+\dfrac{2k\pi}{3};\, \dfrac{2\pi}{3}+2k\pi}\Bigg|\, k\in \mathbb{Z}\right\}}$