resoudre dans R l inequation suivante [tex] \tan(\frac{x}{2} + \frac{5\pi}{6} ) < \frac{ \sqrt{3} }{3} [/tex]

tan(x/2+5π/6)<√3/3
tan(x/2+5π/6)<tan(π/6)
x/2+5π/6<π/6
x/2<-2π/3
x<-4π/3
S=]-8π/3;-4π/3[

Bonsoir,

[tex]\tan\left(\dfrac{x}{2}+\dfrac{5\pi}{6}\right)\ \textless \ \dfrac{\sqrt{3}}{3}\\\\ \tan\left(\dfrac{x}{2}+\dfrac{5\pi}{6}\right)\ \textless \ \tan\left(\dfrac{\pi}{6}\right)\\\\ \dfrac{x}{2}+\dfrac{5\pi}{6}\ \textless \ \dfrac{\pi}{6}\\\\\dfrac{x}{2}\ \textless \ -\dfrac{4\pi}{6}\\\\\dfrac{x}{2}\ \textless \ -\dfrac{2\pi}{3}\\\\x\ \textless \ -\dfrac{4\pi}{3}\\\\\\\boxed{x\in\left]-\dfrac{8\pi}{3};-\dfrac{4\pi}{3}\right[}[/tex]