[Toán 11] Bất phương trình lượng giác

L

lovelycat_handoi95

Pt \Leftrightarrow [TEX](1-sin^2x)cosxsin3x +(1-cos^2x)sinxcos3x < \frac{3}{8}[/TEX]

\Leftrightarrow[TEX] sin3xcosx +sinxcos3x-(sinscosx)(cosxcos3x+sinxsin3x) < \frac{3}{8}[/TEX]

\Leftrightarrow [TEX]sin4x -\frac{1}{2}sin2xcos2x < \frac{3}{8}[/TEX]

\Leftrightarrow [TEX]\frac{3}{4}sin4x< \frac{3}{8}[/TEX]

\Leftrightarrow[TEX] sin4x < \frac{1}{2}[/TEX]

\Leftrightarrow [TEX] -\frac{\pi}{12} +k\frac{\pi}{2} < x < \frac{\pi}{12} +k\frac{\pi}{2} (k \in Z)[/TEX]
 
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