UPSC NDA Math Model Paper 4

Given: 2(cos θ + 1) = 1 and 0 ≤ θ ≤ 2π
⇒ 2cos θ + 2 = 1
⇒ 2cos θ = -1
⇒ cos θ = -1/2
As we know that cos θ is negative in 2‌nd and 3‌rd quadrant and ∵ 0 ≤ θ ≤ 2π
⇒ θ = 2π/3, 4π/3
Hence, θ = 2π/3, 4π/3 are the solution of the given equation.