L9aurinenPauTameyes L9aurinenPauTameyes
  • 11-11-2016
  • Mathematics
contestada

Solve the equation on the interval [0, 2_).

cos x + 2 cos x sin x = 0

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Nirina7
Nirina7 Nirina7
  • 17-11-2016
cos x + 2 cos x sin x = 0, this is equivalent to cos x (1+ 2 sin x) = 0, so 
we have cosx=0 or 
1+ 2 sin x = 0, 
cosx=0, x= arccos(o) = pi/2 + 2kpi
1+ 2 sin x = 0, sinx = - 1/2, implies x=arcsin(- 1/2) = -pi/6 +2kpi
the solution is x=  pi/2 + 2kpi, or x =-pi/6 +2kpi, k is a relative integer
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