Question

(2cos40-cos20)/sin20

Answer 1

Ответ:

     √3

Объяснение:

$frac{2cos40-cos20}{sin20}=frac{cos40+(cos40-cos20)}{sin20}=frac{cos40-2sin(frac{40+20}{2})sin(frac{40-20}{2})}{sin20}=\ =frac{cos40-2sin30sin10}{sin20}=frac{cos40-2*frac{1}{2}sin10}{sin20}=frac{cos40-sin10}{sin20}=frac{cos(90-50)-sin10}{sin20}=\=frac{sin50-sin10}{sin20}=frac{2cos(frac{50+10}{2})sin(frac{50-10}{2})}{sin20}=frac{2cos30sin20}{sin20}=2cos30=2*frac{sqrt{3}}{2}=sqrt{3}$