Find the general solution of the equation

According to the question,

5cos2θ + 7sin2θ – 6 = 0

We know that,

sin2θ = 1 – cos2θ

Therefore, 5cos2θ + 7(1 – cos2θ) – 6 = 0

⇒ 5cos2θ + 7 – 7cos2θ – 6 = 0

⇒ -2cos2θ + 1 = 0

⇒ cos2θ = ½

Therefore, cos θ = ±1/√2

Therefore, cos θ = cos π/4 or cos θ = cos 3π/4

Since, solution of cos x = cos α is given by

x = 2mπ ± α ∀ m ∈ Z

θ = nπ ± π/4, n ∈ Z