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$Number of solutions of the equation \cos^{2} x + (\frac{\sqrt{3} + 1}{2}) \sin x = \frac{\sqrt{3}}{4} + 1 in the interval [- π, π]$ is

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Correct option is B

Given that cos2x+3+12sinx=34+1⇒1−sin2x+3+12sinx−34−1=0⇒sin2x−3+12sinx+34=0∴on solving, we get sinx=12,32∴ x∈−π,π are π6,5π6,π3,2π3 Number of solutions are 4

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Number of solutions of the equation cos2x+3+12sinx=34+1 in the interval [-π,π]is

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$Number of solutions of the equation \cos^{2} x + (\frac{\sqrt{3} + 1}{2}) \sin x = \frac{\sqrt{3}}{4} + 1 in the interval [- π, π]$ is