Решите уравнение; sin2x+2cosx=sinx+1

Решите уравнение;
sin2x+2cosx=sinx+1
- Предмет:
  Алгебра
- Автор:
  scarlettci7l
- 6 лет назад

Ответы 1

$sin2x+2cosx=sinx+1 \\ 2sinxcosx+2cosx-sinx-1=0 \\ (2sinxcosx+2cosx)-(sinx+1)=0 \\ 2cosx(sinx+1)-1(sinx+1)=0 \\ (sinx+1)(2cosx-1)=0$ sinx+1=0 или 2cosx-1=0sinx=-1 2cosx=1x = -π/2+2πn;n∈z cosx=1/2 x=+-π/3+2πn;n∈zОтвет: x= -π/2+2πn;n∈z x=+-π/3+2πn;n∈z
- Автор:
  callie
- 6 лет назад
- 0
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Решите уравнение; sin2x+2cosx=sinx+1

Ответы 1

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Решите уравнение;
sin2x+2cosx=sinx+1