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

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