what set  of values of x would satisfy the inequation sin 3x< sinx 

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$$\begin{gathered} \mathrm{Given}, \\ \sin 3\mathrm{x}<\mathrm{sinx} \\ 3\mathrm{sinx}-4{\sin }^3\mathrm{x}<\mathrm{sinx} \\ 2\mathrm{sinx}-4{\sin }^3\mathrm{x}<0 \\ 2\mathrm{sinx}\left(1-2{\sin }^2\mathrm{x}\right)<0 \\ \mathrm{sinx}<0 \\ \mathrm{or} \\ 1-2{\sin }^2\mathrm{x}<0 \\ 2{\sin }^2\mathrm{x}>1 \\ {\sin }^2\mathrm{x}>\frac{1}{2} \\ \mathrm{sinx}>\frac{1}{\sqrt{2}} \\ \mathrm{or} \mathrm{sinx}<\frac{-1}{\sqrt{2}} \\ \mathrm{taking} \mathrm{intersection} \mathrm{of} \mathrm{both} \mathrm{we} \mathrm{get}, \\ \mathrm{sinx}<\frac{-1}{\sqrt{2}} \\ \mathrm{or} \\ \mathrm{sinx}>\frac{1}{\sqrt{2}} \\ \mathrm{using} \mathrm{trig} \mathrm{circle} \mathrm{we} \mathrm{get}: \\ \mathrm{x}\in \left(\frac{5\mathrm{\pi }}{4},\frac{7\mathrm{\pi }}{4}\right)\cup \left(\frac{\mathrm{\pi }}{4},\frac{3\mathrm{\pi }}{4}\right) \end{gathered}$$

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