Question

radical 3 ctg ( x -pi/2)+3=0 va rog frumos !

Answer 1

$\displaystyle\\ \sqrt{3}~ \text{ctg}\left(x-\frac{\pi}{2}\right) +3=0\\\\ \sqrt{3}~ \text{ctg}\left(x-\frac{\pi}{2}\right) =-3\\\\ \text{ctg}\left(x-\frac{\pi}{2}\right) =-\frac{3}{\sqrt{3}}\\\\ \text{ctg}\left[-\left(\frac{\pi}{2}-x\right)\right] =-\frac{3}{\sqrt{3}}\\\\ \text{-ctg}\left(\frac{\pi}{2}-x\right)=-\frac{3}{\sqrt{3}}\\\\ \text{ctg}\left(\frac{\pi}{2}-x\right)=\frac{3}{\sqrt{3}}\\\\ \text{tg }x=\frac{3}{\sqrt{3}}\\\\ \text{tg }x=\sqrt{3}\\\\ x=\boxed{\frac{\pi}{3} +k\pi}$