Find all solutions to the equation 2cos x 3 sin2 x on 0 2

Find all solutions to the equation 2cos x + 3 = sin^2 x on [0, 2 pi], rounding your answers to three decimal places. x = 1 144 or x = 5.139 x = 0, x = pi, or x = 2 pi The equation has no solutions. x= 0.730 or x = 2.412

Solution

2cosx +3 = sin^2x

RHs : sin^2x = 1-cos^2x

So, 2cosx +3 = 1-cos^2x

cos^2x +2cosx +2 =0

let cosx =y :

y^2 +2y +2 =0

y has comlex roots as b^2-4ac = 4 - 4*2 = -2

So, given equation has no solution

Option (C)