b). Sinx + sin3x + sin4x = 0 c) 2cosx.cos2x = 1 + cos2x + cos3x

a) `sinx+sin3x+sin4x = 0`  

`<=> 2sin2xcosx + 2sin2xcos2x =0`   

`<=> sin2x(cosx + cos2x)=0` 

`<=>` \(\left[ \begin{array}{l}sin2x=0\\cosx=cos2x\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}2x=kπ\\x= \pm 2x + k2π\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=\dfrac{kπ}{2}\\x=k2π\\x=\dfrac{k2π}{3}\end{array} \right.\)

Vậy PT có 2 họ nghiệm : `x = (kπ)/2` và `x = (k2π)/3`

b) `2cosx . cos2x = 1 + cos2x + cos3x`

`<=> cosx + cos3x = 1 + 2cos^2x – 1 + cos3x`

`<=> 2cos^2x – cosx =0`

`<=> cosx(2cosx-1) =0`

`<=>` \(\left[ \begin{array}{l}cosx=0\\cosx=\dfrac{1}{2}\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=\dfrac{π}{2}+kπ\\x=\pm \dfrac{π}{3}+k2π\end{array} \right.\) 

Vậy PT có 2 họ nghiệm: `x=π/2 + kπ` và `x = π/3 + kπ`