Question Number 143105 by mathdanisur last updated on 10/Jun/21
$$\frac{{cos}\left(\mathrm{3}{x}\right)}{{sin}\left(\mathrm{2}{x}\right)}\:=\:\mathrm{0} \\ $$
Commented by Dwaipayan Shikari last updated on 10/Jun/21
$${cos}\left(\mathrm{3}{x}\right)=\mathrm{0}\:\:\: \\ $$$$\mathrm{3}{x}=\left(\mathrm{2}{k}+\mathrm{1}\right)\frac{\pi}{\mathrm{2}}\Rightarrow{x}=\left(\mathrm{2}{k}+\mathrm{1}\right)\frac{\pi}{\mathrm{6}}\:\:\:\:{k}\in\mathbb{Z} \\ $$$${sin}\left(\mathrm{2}{x}\right)\neq\mathrm{0} \\ $$$$\mathrm{2}{x}\neq{g}\pi\Rightarrow{x}\neq\frac{{g}\pi}{\mathrm{2}} \\ $$$$\left(\mathrm{2}{k}+\mathrm{1}\right)\frac{\pi}{\mathrm{6}}\neq\frac{{g}\pi}{\mathrm{2}}\Rightarrow\mathrm{2}{k}+\mathrm{1}\neq\mathrm{3}{g}\Rightarrow\frac{\mathrm{2}{k}+\mathrm{1}}{\mathrm{3}}\neq{g} \\ $$