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Cos x (2 sin x +1)= 0

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Answer to a math question Cos x (2 sin x +1)= 0

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Hermann
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To solve the equation \cos(x)(2\sin(x)+1) = 0 , we can set each factor equal to zero:

1. Set \cos(x) = 0 :
\cos(x) = 0
x = \frac{\pi}{2} + k\pi where k is an integer.

2. Set 2\sin(x) + 1 = 0 :
2\sin(x) + 1 = 0
2\sin(x) = -1
\sin(x) = -\frac{1}{2}
x = \frac{7\pi}{6} + 2k\pi, \ \frac{11\pi}{6} + 2k\pi where k is an integer.

\boxed{x = \frac{\pi}{2} + k\pi, \ \frac{7\pi}{6} + 2k\pi, \ \frac{11\pi}{6} + 2k\pi}

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