вправа 15.38 гдз 10 клас математика Істер 2018

Умова:

Відповідь - ГДЗ:

1) 2sin70°sin50° + cos160° = cos20° - cos120° + cos160° =
= cos20° + 0,5 + cos(180° - 20°) = cos20° - cos20° + 0,5 = 0,5;
2) 4sin10° + 1/cos40° = (4sin10°cos10°) / cos10° + 1/cos40° =
= (2sin20°cos20°) / (cos10°cos20°) + 1/cos40° =
= sin40°/(cos10°cos20°) + 1/cos40° =
= (sin40°cos40°+cos10°cos20°) / (cos10°cos0°cos40°) =
= (1/2 sin80°+cos10°cos20°) / (cos10°cos20°cos40°) =
= (1/2 sin(90°-10°)+cos10°cos20° / (cos10°cos20°cos40°) =
= (1/2 cos10°+cos10°cos20°) / (1/2 (cos20°+cos60°) =
= (1/2 cos10°(cos20°+cos20°) / (1/2 cos10°(cos20°+1/2) = 1/(1/2) = 2.