Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 192270 by universe last updated on 13/May/23

 prove that    sin 50° + sin 10° = cos 20°

$$\:{prove}\:{that} \\ $$$$\:\:\mathrm{sin}\:\mathrm{50}°\:+\:\mathrm{sin}\:\mathrm{10}°\:=\:\mathrm{cos}\:\mathrm{20}° \\ $$

Answered by Frix last updated on 13/May/23

sin (60°−10°) +sin 10°=  =sin 60° cos 10° −cos60° sin 10° +sin 10° =  =(((√3)cos 10°)/2)+((sin 10°)/2)=sin (10°+60°) =  =sin 70° =cos 20°

$$\mathrm{sin}\:\left(\mathrm{60}°−\mathrm{10}°\right)\:+\mathrm{sin}\:\mathrm{10}°= \\ $$$$=\mathrm{sin}\:\mathrm{60}°\:\mathrm{cos}\:\mathrm{10}°\:−\mathrm{cos60}°\:\mathrm{sin}\:\mathrm{10}°\:+\mathrm{sin}\:\mathrm{10}°\:= \\ $$$$=\frac{\sqrt{\mathrm{3}}\mathrm{cos}\:\mathrm{10}°}{\mathrm{2}}+\frac{\mathrm{sin}\:\mathrm{10}°}{\mathrm{2}}=\mathrm{sin}\:\left(\mathrm{10}°+\mathrm{60}°\right)\:= \\ $$$$=\mathrm{sin}\:\mathrm{70}°\:=\mathrm{cos}\:\mathrm{20}° \\ $$

Answered by mehdee42 last updated on 13/May/23

2sin(((50+10)/2))cos(((50−10)/2))=2sin30cos20=cos20

$$\mathrm{2}{sin}\left(\frac{\mathrm{50}+\mathrm{10}}{\mathrm{2}}\right){cos}\left(\frac{\mathrm{50}−\mathrm{10}}{\mathrm{2}}\right)=\mathrm{2}{sin}\mathrm{30}{cos}\mathrm{20}={cos}\mathrm{20} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com