chia 2 vế pt cho 2 đc:
pt\(\Leftrightarrow\dfrac{1}{2}cos7x-\dfrac{\sqrt{3}}{2}sin7x=-\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow-sin\dfrac{\pi}{6}cos7x+cos\dfrac{\pi}{6}sin7x=\dfrac{\sqrt{2}}{2}\\ \Leftrightarrow sin\left(7x-\dfrac{\pi}{6}\right)=sin\dfrac{\pi}{4}\)
\(\Leftrightarrow7x-\dfrac{\pi}{6}=\dfrac{\pi}{4}+k2n\) hay \(7x-\dfrac{\pi}{6}=\dfrac{3\pi}{4}+h2\pi\) (k,h ∈ Z)
\(\Leftrightarrow x=\dfrac{5\pi}{84}+\dfrac{k2\pi}{7}\) hay \(x=\dfrac{11\pi}{84}+\dfrac{h2\pi}{7}\)
(k,h ∈ Z)
Do \(x\in\left(\dfrac{2\pi}{5};\dfrac{6\pi}{7}\right)\) nen
\(\dfrac{2\pi}{5}< \dfrac{5\pi}{84}< \dfrac{k2\pi}{7}< \dfrac{6\pi}{7}\) hay \(\dfrac{2\pi}{5}< \dfrac{11\pi}{84}< \dfrac{h2\pi}{7}< \dfrac{6\pi}{7}\left(k,h\in Z\right)\)
\(\Leftrightarrow\dfrac{2}{5}< \dfrac{5}{84}< \dfrac{k2}{7}< \dfrac{6}{7}\) hay \(\dfrac{2}{5}< \dfrac{11}{84}< \dfrac{h2}{7}< \dfrac{6}{7}\)
\(\Rightarrow k=2,h=1,2\)
vạy \(x=\dfrac{5\pi}{84}+\dfrac{4\pi}{7}=\dfrac{53}{84}\pi\)
\(x=\dfrac{11\pi}{84}+\dfrac{2\pi}{7}=\dfrac{35}{84}\pi\)
\(x=\dfrac{11\pi}{84}+\dfrac{4\pi}{7}=\dfrac{59}{84}\pi\)
