10*cos^(2)*x+3*cosx=1

Question

10*cos^(2)*x+3*cosx=1

Answer 1

10cos²x + 3cosx - 1 = 0

заменим cosx на букву а

cosx = a

10a² + 3a - 1 = 0

-3±√(9+40) / 20

a1 = -3+7 /20 = 1/5

a2 = -3-7/20 = -1/2

1) cosx = 1/5

x = ±arccos1/5 + 2πn

2) cosx = -1/2

x = ±(π-arccos1/2) + 2πn

x = ±2π/3 + 2πn