85.
ĐKXĐ: \(\left\{{}\begin{matrix}x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x\ne\dfrac{\pi}{6}+\dfrac{k\pi}{3}\end{matrix}\right.\)
\(tan3x=\dfrac{1}{tan2x}\)
\(\Rightarrow tan3x=cot2x\)
\(\Rightarrow tan3x=tan\left(\dfrac{\pi}{2}-2x\right)\)
\(\Rightarrow3x=\dfrac{\pi}{2}-2x+k\pi\)
\(\Rightarrow x=\dfrac{\pi}{10}+\dfrac{k\pi}{5}\)
Nghiệm âm lớn nhất là \(x=\dfrac{\pi}{10}-\dfrac{\pi}{5}=-\dfrac{\pi}{10}\)
86.
ĐKXĐ: \(x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)
\(\dfrac{cos4x}{cos2x}=\dfrac{sin2x}{cos2x}\)
\(\Rightarrow cos4x=sin2x\)
\(\Leftrightarrow1-2sin^22x=sin2x\)
\(\Leftrightarrow2sin^22x+sin2x-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin2x=-1\left(loại\right)\\sin2x=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{\pi}{6}+k2\pi\\2x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{12}+k\pi\\x=\dfrac{5\pi}{12}+k\pi\end{matrix}\right.\)
\(\Rightarrow\) Nghiệm lớn nhất \(x=\dfrac{5\pi}{12}\)
