Question

2sinxcosx+ 5cos²x -4 = 0

Answer 1

Pt \(\Leftrightarrow5cos^2x+2sinx.cosx-4\left(sin^2x+cos^2x\right)=0\)

\(\Leftrightarrow cos^2x+2sinx.cosx-4sin^2x=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=\left(-1-\sqrt{5}\right)sinx\\cosx=\left(-1+\sqrt{5}\right)sinx\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}cotx=-1-\sqrt{5}\\cotx=-1+\sqrt{5}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=arc.cot\left(-1-\sqrt{5}\right)+k\pi\\x=arc.cot\left(-1+\sqrt{5}\right)+k\pi\end{matrix}\right.\)(\(k\in Z\))

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