2 cos^2 x - cos x = 0

Question

find the exact solutions in the interval 0, 2pi

Answer 1

2cos²x - cos x = 0

cos x (2cos x - 1) = 0

 

cos x = 0

x = π/2, 3π/2

 

2cos x - 1 = 0

2cos x = 1

cos x = 1/2

x = π/3, 5π/3

 

Answer 2

2cos^2x - cos x = cos x*(2cos x - 1) = 0 -> cos x = 0, or cos x = 1/2 -> x = pi/2,3pi/2,pi/3,5pi/3, x⊂[0,2pi].