ĐKXĐ: \(x\ne-\dfrac{\pi}{4}+k\pi\)
\(\dfrac{cos4x-cos2x+2sin^2x}{sinx+cosx}=0\)
\(\Rightarrow cos4x-cos2x+2sin^2x=0\)
\(\Leftrightarrow2cos^22x-1-cos2x+1-cos2x=0\)
\(\Leftrightarrow cos^22x-cos2x=0\)
\(\Rightarrow\left[{}\begin{matrix}cos2x=0\\cos2x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x=k\pi\end{matrix}\right.\)
Kết hợp ĐKXĐ \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+k\pi\\x=k\pi\end{matrix}\right.\)
ĐKXĐ: \(\sqrt{2}sin\left(x+\dfrac{pi}{4}\right)< >0\)
=>x+pi/4<>kpi
=>x<>-pi/4+kpi
\(PT\Rightarrow cos4x-\left(1-2sin^2x\right)+2sin^2x=0\)
=>\(cos4x-1+4sin^2x=0\)
=>\(2cos^22x-1-1+4\cdot\dfrac{1-cos2x}{2}=0\)
=>\(2cos^22x-2+2-2cos2x=0\)
=>2 cos 2x(cos2x-1)=0
=>cos2x=0 hoặc cos2x=1
=>2x=pi/2+kpi hoặc 2x=k2pi
=>x=pi/4+kpi/2 hoặc x=kpi
=>x=pi/4+kpi hoặc x=kpi
