Find all sollutions of the equation cos x2 sin x 1 0 on th

Find all sollutions of the equation cos x(2 sin x + 1) = 0. on the interval [0, 2pi). The answers are A, B, C and D where 0

cos x ( 2*sin x +1) = 0

either cos x = 0

cos x = cos n*pi/2 n = 1,3 lie in range

cos x = cos pi/2 or cos x = cos 3*pi/2

x = pi/2 , 3*pi/2

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2*sin x + 1 = 0

2*sin x = -1

sin x = -1/2

sin x = - sin pi/6

sin x = sin ( pi + pi/6) or sin x = sin (2 pi - pi/6)

x = 7*pi / 6 x = 11 pi/6

ans A = pi/2, B = 3pi/2, C = 7pi/6, D = 11 pi/6