Solve the following equation for 0 ≤ x ≤ 360 2cos⁡x = sin^2 x + 2

Question

Solve the following equation for 0⁰ ≤ x ≤ 360⁰ 2cos⁡x = sin² x + 2

Answer 1

2 cos x = 1 - cos²x + 2
cos²x + 2cosx - 3 = 0
p = cos x
p² + 2p -3 = 0
p² + 3p -p -3 =0
p(p+3) - 1(p+3) =0 
p = 1 or -3
cos x = 1
x=0º, 360º