a/
\(\Leftrightarrow2cos^22x+2cos^2x-1=0\)
\(\Leftrightarrow2cos^22x+cos2x=0\)
\(\Leftrightarrow cos2x\left(2cos2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\cos2x=-\frac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=\frac{\pi}{2}+k\pi\\2x=\pm\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+\frac{k\pi}{2}\\x=\pm\frac{\pi}{3}+k\pi\end{matrix}\right.\)
b/
\(\Leftrightarrow2cos^2x-1+1-cos^2x-2cosx+1=0\)
\(\Leftrightarrow cos^2x-2cosx+1=0\)
\(\Leftrightarrow\left(cosx-1\right)^2=0\)
\(\Rightarrow cosx=1\Rightarrow x=k2\pi\)
c/
\(4\left(1+tan^2x\right)+tanx-7=0\)
\(\Leftrightarrow4tan^2x+tanx-3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=1\\tanx=-\frac{3}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+k\pi\\x=arctan\left(-\frac{3}{4}\right)+k\pi\end{matrix}\right.\)
d/
\(\Leftrightarrow3\left(1-cos2x\right)-2\left(1-cos^22x\right)=5\)
\(\Leftrightarrow2cos^22x-3cos2x-4=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=\frac{3+\sqrt{41}}{4}\left(l\right)\\cos2x=\frac{3-\sqrt{41}}{4}\end{matrix}\right.\)
\(\Rightarrow x=\pm\frac{1}{2}arccos\left(\frac{3-\sqrt{41}}{4}\right)+k\pi\)
Nghiệm xấu quá :(
e/
\(\Leftrightarrow3\left(1-cos6x\right)-\left(2cos^26x-1\right)=4\)
\(\Leftrightarrow-2cos^26x-3cos6x=0\)
\(\Leftrightarrow cos6x\left(2cos6x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}cos6x=0\\cos6x=-\frac{3}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow6x=\frac{\pi}{2}+k2\pi\)
\(\Rightarrow x=\frac{\pi}{12}+\frac{k\pi}{3}\)
