Решите уравнение cosx + 2cos2x = 1

Question

Решите уравнение cosx + 2cos2x = 1

Answer 1

cosx + 2cos2x = 1

-2sin^2(x)+2cos^2(x)+cos(x)=1

  n Е Z

   n Е Z

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Answer 2

cosx + 2cos2x = 1

2cos3x = 1

cos3x = 1/2

3x = +-arccos 1/2 + 2Пn

3x = +- П/3 + 2Пn

x = +- П/6 + 2Пn/3,   n Є Z