Question

Nghiệm của phương trình cot\(\dfrac{x}{2}\)= \(\dfrac{1}{\sqrt{3}}\)

Giúp mình với ạ 

Answer 1

\(cot\dfrac{x}{2}=\dfrac{1}{\sqrt{3}}\)

\(\Leftrightarrow cot\dfrac{x}{2}=cot\left(\dfrac{\pi}{3}\right)\)

\(\Rightarrow\dfrac{x}{2}=\dfrac{\pi}{3}+k\pi\)

\(\Rightarrow x=\dfrac{2\pi}{3}+k2\pi\)

Answer 2

ĐKXĐ: \(\dfrac{x}{2}\ne k\Omega\)

=>\(x\ne k2\Omega\)

\(cot\left(\dfrac{x}{2}\right)=\dfrac{1}{\sqrt{3}}\)

=>\(tan\left(\dfrac{x}{2}\right)=\sqrt{3}\)

=>\(\dfrac{x}{2}=\dfrac{\Omega}{3}+k\Omega\)

=>\(x=\dfrac{2}{3}\Omega+2k\Omega\)