\(\Leftrightarrow2cos^23x+2cos^24x+2cos^25x=3\)
\(\Leftrightarrow cos6x+1+cos8x+1+cos10x+1=3\)
\(\Leftrightarrow cos6x+cos10x+cos8x=0\)
\(\Leftrightarrow2cos8x.cos2x+cos8x=0\)
\(\Leftrightarrow cos8x\left(2cos2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos8x=0\\cos2x=-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{16}+\frac{k\pi}{8}\\x=\frac{\pi}{3}+k\pi\\x=-\frac{\pi}{3}+k\pi\end{matrix}\right.\)
Ủ uôi, chữ đẹp thía mồ, chả bù cho tui, mới bị chê chữ xong :(
\(\cos10x=2\cos^25x-1;\cos8x=2\cos^24x-1;\cos6x=2\cos^23x-1\)\(\Rightarrow\frac{\cos6x+1}{2}+\frac{\cos8x+1}{2}+\frac{\cos10x+1}{2}=1,5\)
\(\Leftrightarrow\left(\cos6x+\cos10x\right)+\cos8x=0\)
\(\Leftrightarrow2\cos2x\cos8x+\cos8x=0\)
Đến đây đơn giản r nhó
