`c)`
\(\left\{ \begin{array}{l}sin (\dfrac{π}{6} - \dfrac{x}{3}) \ne 0 \\sin 2x - 1 \ne 0\end{array} \right.\)
`<=>` \(\left\{ \begin{array}{l}\dfrac{π}{6} - \dfrac{x}{3} \ne kπ\\2x \ne \dfrac{π}{2} + k2π\end{array} \right.\)
`<=>` \(\left\{ \begin{array}{l}x \ne \dfrac{π}{2} + k3π\\x \ne \dfrac{π}{4} + kπ\end{array} \right.\) `(k ∈ ZZ)`
`=> D = RR \\ {π/2 + k3π; π/4 + kπ | k ∈ ZZ}`
`d)`
`sin 3x - sin(π/3 - x) ne 0`
`<=> sin 3x ne sin (π/3 - x)`
`<=>` \(\left[ \begin{array}{l}3x \ne \dfrac{π}{3} - x + k2π\\3x \ne x - \dfrac{π}{3} + k2π\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x \ne \dfrac{π}{12} + k\dfrac{π}{4}\\x \ne -\dfrac{π}{6} + kπ\end{array} \right.\) `(k ∈ ZZ)`
`=> D = RR \\ {π/12 + k(π)/4; -π/6 + kπ | k ∈ ZZ}`
`e)`
`cos (x/2) - cos 3x ne 0`
`<=> cos (x/2) ne cos 3x`
`<=> x/2 ne ±3x + k2π`
`<=> x ne ±6x + k4π`
`<=>` \(\left[ \begin{array}{l}x \ne k\dfrac{4π}{5}\\x \ne k\dfrac{4π}{7}\end{array} \right.\)
`=> D = RR \\ {k(4π)/5; k(4π)/7 | k ∈ ZZ}`
