[TEX](1+cosx)(1+cos2x)(1+cos3x)=\frac{1}{2}[/TEX]
[TEX]pt \leftrightarrow cos^2(\frac{x}{2}).cos^2x.cos^2(\frac{3x}{2})= \frac{1}{16}[/TEX]
[TEX]x=2k\pi[/TEX] không là nghiệm
[TEX]x \neq 2k\pi \longrightarrow sin(\frac{x}{2}) \neq 0[/TEX]
[TEX]\longrightarrow pt \leftrightarrow sin^2x.cos^2x.cos^2(\frac{3x}{2}) = \frac{sin^2(\frac{x}{2})}{4}[/TEX]
[TEX]\leftrightarrow sin^22x.cos^2(\frac{3x}{2}) = sin^2(\frac{x}{2})[/TEX]
[TEX]\leftrightarrow (sin2x.cos(\frac{3x}{2}))^2 = sin^2(\frac{x}{2})[/TEX]
[TEX]\leftrightarrow (sin(\frac{7x}{2})+sin(\frac{x}{2}))^2 = 4sin^2(\frac{x}{2})[/TEX]
[TEX]\leftrightarrow \left[\begin sin(\frac{7x}{2})+sin(\frac{x}{2}) = 2sin(\frac{x}{2}) \\ sin(\frac{7x}{2})+sin(\frac{x}{2}) = -2sin(\frac{x}{2})[/TEX]
[TEX]\leftrightarrow \left[\begin sin(\frac{7x}{2})=sin(\frac{x}{2}) \\ {sin(\frac{7x}{2}) = sin(\frac{-x}{2})[/TEX]