65.
\(cotx=\dfrac{1}{\sqrt{3}}\Rightarrow x=\dfrac{\pi}{3}+k\pi\)
Nghiệm âm lớn nhất là \(\dfrac{\pi}{3}+\pi.\left(-1\right)=-\dfrac{2\pi}{3}\)
66.
\(cos\left(3x-\dfrac{\pi}{6}\right)=sin\left(2x+\dfrac{\pi}{3}\right)\)
\(\Leftrightarrow cos\left(3x-\dfrac{\pi}{6}\right)=cos\left(\dfrac{\pi}{6}-2x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-\dfrac{\pi}{6}=\dfrac{\pi}{6}-2x+k2\pi\\3x-\dfrac{\pi}{6}=2x-\dfrac{\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{15}+\dfrac{k2\pi}{5}\\x=k2\pi\end{matrix}\right.\)
\(\Rightarrow x=\left\{\dfrac{\pi}{15};\dfrac{7\pi}{15};\dfrac{13\pi}{15};\dfrac{19\pi}{15}\right\}\)
67.
\(sinx.cosx=\dfrac{1}{2}\)
\(\Leftrightarrow2sinx.cosx=1\)
\(\Leftrightarrow sin2x=1\)
\(\Leftrightarrow2x=\dfrac{\pi}{2}+k2\pi\)
\(\Leftrightarrow x=\dfrac{\pi}{4}+k\pi\)
\(0< x< \pi\Rightarrow0< \dfrac{\pi}{4}+k\pi< \pi\)
\(\Rightarrow k=0\)
\(\Rightarrow x=\dfrac{\pi}{4}\)
