Question Number 144822 by mathlove last updated on 29/Jun/21
$$\mathrm{sin}\:^{\mathrm{3}} {x}\mathrm{cos}\:{x}−\mathrm{cos}\:^{\mathrm{3}} {x}\mathrm{sin}\:{x}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${x}=? \\ $$
Answered by ajfour last updated on 29/Jun/21
$$\mathrm{2sin}\:{x}\mathrm{cos}\:{x}\left(\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{cos}\:^{\mathrm{2}} {x}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{2sin}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{2}{x}=−\mathrm{1} \\ $$$$\mathrm{sin}\:\mathrm{4}{x}=−\mathrm{1} \\ $$$$\mathrm{4}{x}=\mathrm{2}{n}\pi−\frac{\pi}{\mathrm{2}} \\ $$$${x}=\frac{{n}\pi}{\mathrm{2}}−\frac{\pi}{\mathrm{8}} \\ $$
Commented by mathlove last updated on 29/Jun/21
$${thanks}\:{sir} \\ $$