Question Number 11274 by uni last updated on 18/Mar/17
$$\frac{{sin}\mathrm{20}+\sqrt{\mathrm{3}}×{cos}\mathrm{20}}{{cos}\mathrm{10}}=? \\ $$
Answered by bahmanfeshki1 last updated on 18/Mar/17
$${sin}\:\mathrm{20}+\sqrt{\mathrm{3}}×{cos}\mathrm{20}=\mathrm{2}×{cos}\left(\mathrm{30}−\mathrm{20}\right)=\mathrm{2}×{cos}\mathrm{10} \\ $$$$\Rightarrow\frac{\mathrm{2}{cos}\mathrm{10}}{{cos}\mathrm{10}}=\mathrm{2} \\ $$
Answered by malwaan last updated on 19/Mar/17
$$\frac{\mathrm{2}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×{cos}\mathrm{20}+\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{sin20}\right)}{\mathrm{cos10}} \\ $$$$=\frac{\mathrm{2}\left(\mathrm{cos30cos20}+\mathrm{sin30sin20}\right)}{\mathrm{cos10}} \\ $$$$=\frac{\mathrm{2cos}\left(\mathrm{30}−\mathrm{20}\right)}{\mathrm{cos10}}=\frac{\mathrm{2cos10}}{\mathrm{cos10}}=\mathrm{2} \\ $$