Question

Giải phương trình: \(3\cot^2x+2\sqrt{2}\sin^2x=\left(2+3\sqrt{2}\right)\cos x\)

Answer 1

ĐKXĐ: ...

\(\Leftrightarrow3cos^2x+2\sqrt{2}sin^4x=\left(2+3\sqrt{2}\right)cosx.sin^2x\)

\(\Leftrightarrow3cos^2x-3\sqrt{2}cosx.sin^2x+2\sqrt{2}sin^4x-2cosx.sin^2x=0\)

\(\Leftrightarrow3cosx\left(cosx-\sqrt{2}sin^2x\right)-2sin^2x\left(cosx-\sqrt{2}sin^2x\right)=0\)

\(\Leftrightarrow\left(3cosx-2sin^2x\right)\left(cosx-\sqrt{2}sin^2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3cosx-2sin^2x=0\\cosx-\sqrt{2}sin^2x=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}3cosx-2\left(1-cos^2x\right)=0\\cosx-\sqrt{2}\left(1-cos^2x\right)=0\end{matrix}\right.\)