The smallest positive angle which satisfies the equation 2sin^2x + √3 cosx + 1 = 0 is ​

Question

The smallest positive angle which satisfies the equation 2sin²x + \(\sqrt3\)cosx + 1 = 0 is

A. \(\frac{5π}6\)

B. \(\frac{2π}3\)

C. \(\frac{π}3\)

D. \(\frac{π}6\)

Answer 1

2(1 - cos²x)+√3cos x +1 = 0 

2 - 2 cos²x + √3cos x +1 = 0 

2 cos²x - √3cos x -3 = 0

cosx = \(\sqrt3\) or \(\frac{-\sqrt3}2\)

x = π - \(\frac{π}6\)

x = \(\frac{5π}6\)

Option A