вправа 14.6 гдз 10 клас математика Істер 2018

Умова:

Відповідь - ГДЗ:

1) cos5°/sin10° = cos5°/(2sin5°cos5°) = 1/(2sin5°);
2) sin100°/2sin50° = (2sin50°cos50°)/2sin50° = cos50°;
3) (cos20°+sin20°)/cos40° =
= (cos20°+sin20°)/(cos220°-sin220°) =
= (cos20°+sin20°)/((cos20°+sіn20гр)cos(20°-sin20°)) =
= 1/(cos20°-sin20°);
4) cos140°/(sin70°-cos70°) =
= (cos²70°-sin²70°)/(sin70°-cos70°) =
= ((cos70°-sin70°)(cos70°+sin70°))/(sin70°-cos70°) =
= cos70° + sіn70°.