General solution of the equation 4 cot ⁡ 2 θ + t a n 2 θ = cot 2 ⁡ θ is (where, n ∈ Z )

Step-by-step solution

The given equation can be written as 2 1 - t a n 2 θ tan ⁡ θ + t a n 2 θ = 1 t a n 2 θ ⇒   2 1 - t a n 2 θ + t a n 3 θ tan ⁡ θ = 1 t a n 2 θ ⇒ 2 1 - t a n 2 θ tan ⁡ θ + t a n 4 θ - 1 = 0 ⇒ 1 - t a n 2 θ 2 tan ⁡ θ - 1 - t a n 2 θ = 0 ⇒ 1 - t a n 2 θ 1 - tan ⁡ θ 2 = 0 ⇒ 1 + tan ⁡ θ 1 - tan ⁡ θ 3 = 0 ⇒    tan ⁡ θ = ± 1