General solution of the equation t a n 2 θ + s e c 2 θ = 1 is

Step-by-step solution

Using, s e c 2 θ = 1 c o s 2 θ = 1 + t a n 2 θ 1 - t a n 2 θ ⇒ We can write the given equation as t a n 2 θ + 1 + t a n 2 θ 1 - t a n 2 θ = 1 ⇒ t a n 2 θ ( 1 - t a n 2 θ ) + 1 + t a n 2 θ = 1 - t a n 2 θ ⇒ 3 t a n 2 θ - t a n 4 θ = 0 ⇒ t a n 2 θ ( 3 - t a n 2 θ ) = 0 ⇒ t a n θ = 0 or tan 2 θ = 3 = ( 3 ) 2 ⇒ tanθ = 0 ⇒ θ = m π, m ∈ I or tan 2 θ = tan 2 π 3 ⇒ θ = n π ± π 3 , n ∈ I