Question

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

Answer 1

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

Answer 2

w = π/2

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