` a) ` ` cos5xsin4x = cos3xcos2x `
` <=> 1/2 . (cosx + cos9x) = 1/2 . (cosx + cos5x) `
` <=> \frac{cosx}{2} + \frac{cos9x}{2} = \frac{cosx}{2} + \frac{cos5x}{2} `
` <=> \frac{cos9x}{2} = \frac{cos5x}{2} `
` <=> cos9x - cos5x = 0 `
` <=> -2sin7xsin2x = 0 `
` <=> sin7xsin2x = 0 `
` <=> ` \(\left[ \begin{array}{l}sin7x=0\\sin5x=0\end{array} \right.\)
` <=> ` \(\left[ \begin{array}{l}x=\frac{kπ}{7}\\x=\frac{kπ}{2}\end{array} \right.\) `(k ∈ Z)`
` b) ` ` sinx + sin2x = cosx + cos2x `
` <=> 2sin\frac{3x}{2}cos\frac{-x}{2}=2cos\frac{3x}{2}cos\frac{-x}{2} `
` <=> sin\frac{3x}{2}cos\frac{x}{2}=cos\frac{3x}{2}cos\frac{x}{2} `
` <=> sin\frac{3x}{2}cos\frac{x}{2} - cos\frac{3x}{2}cos\frac{x}{2} = 0 `
` <=> cos\frac{x}{2}(sin\frac{3x}{2} - cos\frac{3x}{2}) = 0 `
` <=> ` \(\left[ \begin{array}{l}cos\frac{x}{2}=0\\sin\frac{3x}{2}-cos\frac{3x}{2}=0\end{array} \right.\)
` <=> ` \(\left[ \begin{array}{l}x=π+2kπ\\x=\frac{π}{6}+\frac{2kπ}{3}\end{array} \right.\) `(k ∈ Z)`
