Question

Solve $cos\theta + cos3\theta - 2 cos 2\theta$​

Answer 1

Solution :

Given, cosθ + cos3θ - 2 cos2θ = 0

⇒ (cosθ + cos3θ) - 2 cos2θ = 0

⇒ 2 cos(θ + 3θ)/2 cos(θ - 3θ)/2 - 2 cos2θ = 0

⇒ 2 cos2θ cosθ - 2 cos2θ = 0

⇒ cos2θ (cosθ - 1) = 0

Either cos2θ = 0 or, cosθ - 1 = 0

• cos2θ = 0

⇒ 2θ = (2n + 1) . π/2 , n ∈ ℤ

∴ θ = (2n + 1) . π/4 , n ∈ ℤ

• cosθ - 1 = 0

⇒ cosθ = 1

∴ θ = 2nπ , n ∈ ℤ