Question Number 163938 by cortano1 last updated on 12/Jan/22
$$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(−\mathrm{3}{x}\right)−\mathrm{cos}\:\left(\mathrm{3}{x}\right)}{\mathrm{sin}\:^{\mathrm{2}} \left({x}\sqrt{\mathrm{5}}\:\right)}=? \\ $$
Answered by 770551415 last updated on 12/Jan/22
$$\boldsymbol{{Solution}}:\:{cos}\:{y}\:{is}\:{even}\: \\ $$$$\:\:{cos}\left(−\mathrm{3}{x}\right)={cos}\left(\mathrm{3}{x}\right)\: \\ $$$$\:{cos}\left(−\mathrm{3}{x}\right)−{cos}\left(\mathrm{3}{x}\right)=\mathrm{0} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{l}im}\frac{\mathrm{0}}{{sin}^{\mathrm{2}} \left({x}\sqrt{\mathrm{5}}\right)}=\mathrm{0} \\ $$