Question Number 147134 by mathdanisur last updated on 18/Jul/21
$$\sqrt{\mathrm{2}{sin}\left({x}\right)−\mathrm{1}}\:\centerdot\:{sin}\left({x}\right)\:>\:\mathrm{0} \\ $$
Commented by hknkrc46 last updated on 18/Jul/21
$$\blacktriangleright\:\mathrm{2sin}\:\boldsymbol{{x}}\:−\:\mathrm{1}\:>\:\mathrm{0}\:\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0}\:\equiv\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\blacktriangleright\:\frac{\boldsymbol{\pi}}{\mathrm{6}}\:<\:\boldsymbol{{x}}\:<\:\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{6}}\:\: \\ $$
Commented by mathdanisur last updated on 18/Jul/21
$${thanks}\:{Sir} \\ $$