1)\(sin^23x.cos2x+sin^2x=0\)
2)
\(cos^23x+cos^22x=sin^2x\)
3)
\(\frac{1}{4}+cos^2\frac{x}{3}=\frac{1}{2}sin^2\frac{x}{2}\)
4)
\(sin^23x-sin^22x-sin^2x=0\)
5)
\(2cos^2x=3sin^25x+2\)
6) 3cosx+2cos2x-cos3x=2sinxsin2x-1
7) \(sinx+cosx=\sqrt{2}\left(2-sin^32x\right)\)
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Đọc tiếp
1)\(sin^23x.cos2x+sin^2x=0\)
2)
\(cos^23x+cos^22x=sin^2x\)
3)
\(\frac{1}{4}+cos^2\frac{x}{3}=\frac{1}{2}sin^2\frac{x}{2}\)
4)
\(sin^23x-sin^22x-sin^2x=0\)
5)
\(2cos^2x=3sin^25x+2\)
6) 3cosx+2cos2x-cos3x=2sinxsin2x-1
7) \(sinx+cosx=\sqrt{2}\left(2-sin^32x\right)\)
1.
\(\Leftrightarrow\left(1-cos6x\right)cos2x+1-cos2x=0\)
\(\Leftrightarrow cos2x-cos2x.cos6x+1-cos2x=0\)
\(\Leftrightarrow\frac{1}{2}\left(cos8x-cos4x\right)-1=0\)
\(\Leftrightarrow2cos^24x-cos4x-3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos4x=-1\\cos4x=\frac{3}{2}\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow4x=\pi+k2\pi\)
\(\Leftrightarrow x=\frac{\pi}{4}+\frac{k\pi}{2}\)
3.
Đặt \(\frac{x}{6}=t\Rightarrow\frac{1}{4}+cos^22t=\frac{1}{2}sin^23t\)
\(\Leftrightarrow1+4cos^22t=1-cos6t\)
\(\Leftrightarrow cos6t+4cos^22t=0\)
\(\Leftrightarrow4cos^32t+4cos^22t-3cos2t=0\)
\(\Leftrightarrow cos2t\left(4cos^22t+4cos2t-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2t=0\\cos2t=\frac{1}{2}\\cos2t=-\frac{3}{2}\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}t=\frac{\pi}{4}+\frac{k\pi}{2}\\t=\pm\frac{\pi}{6}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{x}{3}=\frac{\pi}{4}+\frac{k\pi}{2}\\\frac{x}{3}=\frac{\pi}{6}+k\pi\\\frac{x}{3}=-\frac{\pi}{6}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow x=...\)