Câu 28 :
Ta có : \(\cot x=\sqrt{3}\)
\(\Rightarrow x=\dfrac{\pi}{6}+k\pi\)
Mà \(0< x< 2020\pi\)
\(\Rightarrow0< \dfrac{1}{6}+k< 2020\)
\(\Rightarrow-\dfrac{1}{6}< k< \dfrac{12119}{6}\)
\(\Rightarrow k\in\left\{0;1;2;.....;2019\right\}\)
\(\Rightarrow x\in\left\{\dfrac{\pi}{6}+0\pi;......;\dfrac{\pi}{6}+2019\pi\right\}\)
\(\Rightarrow\Sigma x=\dfrac{\pi}{6}+0\pi+.....+\dfrac{\pi}{6}+2019\pi\)
\(=2020.\dfrac{\pi}{6}+2039190\pi\)
Vậy ...
27.
\(tanx=tan\dfrac{3\pi}{11}\)
\(\Leftrightarrow x=\dfrac{3\pi}{11}+k2\pi\)
Ta có: \(\dfrac{\pi}{4}< \dfrac{3\pi}{11}+k2\pi< 2\pi\Leftrightarrow-\dfrac{1}{88}< k< \dfrac{19}{22}\)
Mà \(k\in Z\Rightarrow k=0\)
\(\Rightarrow\) Tổng các nghiệm là \(S=\dfrac{3\pi}{11}\)
