\(\log_{5-x^2}\dfrac{3sin2x-2sinx}{sin2x.cosx}=\)\(\log_{5-x^2}2\left(1\right)\)
ĐKXĐ : \(-\sqrt{5}< x< \sqrt{5}\)
\(\left(1\right)\Leftrightarrow\dfrac{3sin2x-2sinx}{sin2x.cosx}=2\) \(\left(x\ne k\pi;x\ne\dfrac{\pi}{2}+k\pi;k\in Z\right)\)
\(\Leftrightarrow\dfrac{6sinxcosx-2sinx}{2sinx.cos^2x}=2\)
\(\Leftrightarrow\dfrac{2sinx\left(3cosx-1\right)}{2sinx.cos^2x}=2\)
\(\Leftrightarrow3cosx-1=2cos^2x\)
\(\Leftrightarrow2cos^2x-3cosx+1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=1=cos0\\cosx=\dfrac{1}{2}=cos\dfrac{\pi}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\) \(\left(k\in Z\right)\) thỏa mãn \(-\sqrt{5}< x< \sqrt{5}\)
