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Question Number 30054 by rahul 19 last updated on 15/Feb/18

Answered by ajfour last updated on 16/Feb/18

$$let\sin x=s$$$$5s^2+4s^2(1-s^2)-4(1-2s^2)>0$$$$or4{\mathit{s}}^4-17{\mathit{s}}^2+4<0$$$$(4{\mathit{s}}^2-1)({\mathit{s}}^2-4)<0$$$$\Rightarrow \frac{1}{4}<s^2<4andweknow{s}^2⩽1$$$$so\frac{1}{4}<s^2⩽1$$$$\Rightarrow \mathit{n}\mathit{\pi }+\frac{\mathit{\pi }}{6}<\mathit{x}<(\mathit{n}+1)\mathit{\pi }-\frac{\mathit{\pi }}{6}.$$

Commented by rahul 19 last updated on 16/Feb/18

$$\mathrm{thank}\mathrm{u}\mathrm{sir}.$$

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