ĐKXĐ: \(x\ne\frac{k\pi}{2}\)
\(\frac{sinx}{cosx}+\frac{cosx}{sinx}+14=\frac{cos^22x}{sin^22x}\)
\(\Leftrightarrow\frac{2}{sin2x}+14=\frac{1-sin^22x}{sin^22x}\)
Đặt \(sin2x=a\) với \(\left\{{}\begin{matrix}a\ne0\\\left|a\right|\le1\end{matrix}\right.\)
\(\frac{2}{a}+14=\frac{1-a^2}{a^2}\Leftrightarrow15a^2+2a-1=0\) \(\Rightarrow\left[{}\begin{matrix}a=\frac{1}{5}\\a=-\frac{1}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}sin2x=\frac{1}{5}=sin\alpha\\sin2x=-\frac{1}{3}=sin\beta\end{matrix}\right.\) \(\Rightarrow...\)
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