Solve: 2cos^2 (w) - cos (w) - 1=0

w = π/2

Step-by-step explanation:

I used trig identities (double angle) to solve this problem.

Step 1: Rearrange problem

2cos² (w) - cos (w) - 1 = 0

2cos² (w) - 1 - cos (w) = 0

Step 2: Trig Identity

cos2w - cos (w) = 0

Step 3: Combine like terms

cosw = 0

Step 4: Solve

w = cos^-1 (0)

w = π/2

I may have done it wrong so don't rely too much on me

Step-by-step explanation:

2 cos² (w) - cos w-1=0

2 cos² w-2cos w+cos w-1=0

2 cos w (cos w-1) + (cos w-1) = 0

(cos w-1) (2 cos w+1) = 0

either cos w=1=cos 0=cos (0+2nπ)

w=2nπ, n∈I

or 2 cos w+1=0

cos w=-1/2=-cos (π/3) = cos ((2n+1) π±π/3)

w=[ (2n+1) ±1/3]π,

n∈ I