c.
\(\Leftrightarrow2sin^25x+2sin5x.cos5x+4cos^25x=3\)
Nhận thấy \(cos5x=0\) ko phải nghiệm, chia 2 vế cho \(cos^25x\)
\(2tan^25x+2tan5x+4=3\left(1+tan^25x\right)\)
\(\Leftrightarrow tan^25x-2tan5x-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tan5x=1+\sqrt{2}\\tan5x=1-\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=\dfrac{3\pi}{8}+k\pi\\5x=-\dfrac{\pi}{8}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3\pi}{40}+\dfrac{k\pi}{5}\\x=-\dfrac{\pi}{40}+\dfrac{k\pi}{5}\end{matrix}\right.\)
f.
\(\Leftrightarrow\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x=cos4x\)
\(\Leftrightarrow1-\dfrac{1}{2}sin^22x=cos4x\)
\(\Leftrightarrow1-\dfrac{1}{4}\left(1-cos4x\right)=cos4x\)
\(\Leftrightarrow cos4x=1\)
\(\Leftrightarrow4x=k2\pi\)
\(\Leftrightarrow x=\dfrac{k\pi}{2}\)
