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Find all solutions in the interval [0, 2π).

cos2x + 2 cos x + 1 = 0

A. x = 2π
B.x = π
C. x = pi divided by four., seven pi divided by four.
D. x = pi divided by two., three pi divided by two.

Respuesta :

tramserran

Answer: B

Step-by-step explanation:

cos²(x) + 2cos(x) + 1 = 0

Factor to get: (cos x + 1)² = 0

Set each factor equal to zero and solve :

cos x + 1 = 0    ⇒   cos x = -1          

Look at the Unit circle to find when cos = -1

cos = -1 at π

x = π

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