Verified answer

Factor out cos(x):

cos(x)[2sin(x) + 1] = 0

Set each factor to equal zero:

cos(x) = 0

x = π/2, 3π/2

2sin(x) + 1 = 0

2sin(x) = -1

sin(x) = -1/2

x = 7π/6, 11π/6

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Overall:

x = π/2, 3π/2, 7π/6, 11π/6

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http://www.mathway.com/answer.aspx?p=prec?p=2SMB15...

cosx(2sinx+1) = 0

cosx = 0 or sinx = -1/2

x = pi/2, 3pi/2, 7pi/6, 11pi/6