cos5xsin4x=cos3xsin2x sinx+sin2x=cosx+cos2x

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1. ` 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)`

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