Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 11274 by uni last updated on 18/Mar/17

((sin20+(√3)×cos20)/(cos10))=?

$$\frac{{sin}\mathrm{20}+\sqrt{\mathrm{3}}×{cos}\mathrm{20}}{{cos}\mathrm{10}}=? \\ $$

Answered by bahmanfeshki1 last updated on 18/Mar/17

sin 20+(√3)×cos20=2×cos(30−20)=2×cos10  ⇒((2cos10)/(cos10))=2

$${sin}\:\mathrm{20}+\sqrt{\mathrm{3}}×{cos}\mathrm{20}=\mathrm{2}×{cos}\left(\mathrm{30}−\mathrm{20}\right)=\mathrm{2}×{cos}\mathrm{10} \\ $$$$\Rightarrow\frac{\mathrm{2}{cos}\mathrm{10}}{{cos}\mathrm{10}}=\mathrm{2} \\ $$

Answered by malwaan last updated on 19/Mar/17

((2(((√3)/2)×cos20+(1/2)×sin20))/(cos10))  =((2(cos30cos20+sin30sin20))/(cos10))  =((2cos(30−20))/(cos10))=((2cos10)/(cos10))=2

$$\frac{\mathrm{2}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×{cos}\mathrm{20}+\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{sin20}\right)}{\mathrm{cos10}} \\ $$$$=\frac{\mathrm{2}\left(\mathrm{cos30cos20}+\mathrm{sin30sin20}\right)}{\mathrm{cos10}} \\ $$$$=\frac{\mathrm{2cos}\left(\mathrm{30}−\mathrm{20}\right)}{\mathrm{cos10}}=\frac{\mathrm{2cos10}}{\mathrm{cos10}}=\mathrm{2} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com