Не выполняя построений, найдите абциссы точек пересечения графиков функций:

f (x) = cos5xcos (x+pi/6) и g (x) = sin5xsin (x+pi/6) + корень из 3/2

F (x) = cos5x · cos (x + π/6)

g (x) = sin5x · sin (x + π/6) + 0.5√3

cos5x · cos (x + π/6) = sin5x · sin (x + π/6) + 0.5√3

cos5x · cos (x + π/6) - sin5x · sin (x + π/6) = 0.5√3

cos (6x + π/6) = 0.5√3

6x + π/6 = ⁺₋ π/6 + 2πn n∈Z

1) 6x₁ + π/6 = + π/6 + 2πn n∈Z 2) 6x₂ + π/6 = - π/6 + 2πn n∈Z

1) 6x₁ = 2πn n∈Z 2) 6x₂ = - π/3 + 2πn n∈Z

1) x₁ = πn/3 n∈Z 2) x₂ = - π/18 + πn/3 n∈Z

Ответ: x₁ = πn/3 n∈Z

x₂ = - π/18 + πn/3 n∈Z