ĐKXĐ: \(\left\{{}\begin{matrix}x\ne\frac{\pi}{2}+k\pi\\x\ne\frac{\pi}{4}+\frac{k\pi}{2}\end{matrix}\right.\)
\(\frac{a^2}{1-\frac{sin^2x}{cos^2x}}=\frac{sin^2x+a^2-2}{cos^2x-sin^2x}\Leftrightarrow\frac{a^2.cos^2x}{cos^2x-sin^2x}=\frac{sin^2x+a^2-2}{cos^2x-sin^2x}\)
\(\Leftrightarrow a^2\left(1-sin^2x\right)=sin^2x+a^2-2\)
\(\Leftrightarrow\left(a^2+1\right)sin^2x=2\)
\(\Leftrightarrow sin^2x=\frac{2}{a^2+1}\)
Để pt có nghiệm:
\(\Leftrightarrow\left\{{}\begin{matrix}-1< \frac{2}{a^2+1}< 1\\\frac{2}{a^2+1}\ne\frac{\sqrt{2}}{2}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a^2>1\\a^2\ne2\sqrt{2}-1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}a>1\\a< -1\end{matrix}\right.\\a\ne2\sqrt{2}-1\end{matrix}\right.\)
