вправа 15.33 гдз 10 клас математика Істер 2018

Умова:

Відповідь - ГДЗ:

1) sin(3α - π/10)sin(3π/5 - 3α) = 1/2 cos (6α - 7π/10)
sin(3α - π/10) • sin(3π/5 - 3α) =
= 1/2 (cos(3α - π/10 - 3π/5 + 3α) - cos(3α - π/10 + 3π/5 - 3α) =
= 1/2(cos(6α - 7π/10) - cos π/2 = 1/2 cos(6α - 7π/10);
2) 2cos(α - π/4)cos(π/4 + α) = 2cos²α - 1
2cos(α - π/4)cos(π/4 + α) =
= 2 1/2 (cos(α - π/4 - π/4 - α) + cos(α + π/4 + π/4 + α)) =
= (cos π/2 + cos(2α)) = cos2α = 2cos²α - 1.