Решите уравнение: cos^2 x (x+pi/3) = 1

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Алгебра

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20 мая, 00:40

Решите уравнение: cos^2 x (x+pi/3) = 1

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Ответы (2)

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Емельянка · Answer 1

Sin² (x + π/3) = 1

1) sin (x + π/3) = - 1

x + π/3 = - π/2 + 2πk, k ∈z

x = - π/3 - π/2 + 2πk, k ∈z

x = - 5π/6 + 2πk, k ∈z

2) sin (x + π/3) = 1

x + π/3 = π/2 + 2πn, n∈Z

x = - π/3 + π/2 + 2πn, n∈Z

x = π/6 + 2πn, n∈Z

Коста · Answer 2

Cos² (x+π/3) = 1

[1+cos (2x+2π/3) ]/2=1

1+cos (2x+2π/3) = 2

cos (2x+2π/3) = 1

2x+2π/3=2πn

2x=-2π/3+2πn

x=-π/3+πn