Question

Solve the given equation and indicate the number of values of θ sach that 0≤θ<2π satisfy the iquation cos(2θ)+cos(θ)=0

Answer 1

θ = 0 or π/3

Answer 2

cos(2θ)+cos(θ)=0

2cos^2(θ)-1+cos(θ)=0

2cos^2(θ)+cos(θ) -1=0

2cos^2(θ)-2cos(θ)+cos(θ) -1=0

2cosθ [ cosθ-1] +1 [ cos(θ-1]=0

(2cosθ-1)(cosθ-1)=0

cosθ =1/2 or cosθ = 1

θ = π/3 or θ = 0