# Solve 2 cos2 x + 3 sin x = 0

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Solve

2 cos2x + 3 sin x = 0

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Solution: The equation can be written as
2(1− sin2 x) + 3sin x = 0
or 2 sin2 x − 3sin x − 2 = 0
or (2sinx +1) (sinx − 2) =0
Hence sin x = -1/2 or sin x = 2
But sin x = 2 is not possible
Therefore sin x = -1/2 = sin 7π/6
Hence, the solution is given by
x = nπ + (-1)n7π/6, where n ∈ Z.

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