If set A = x :   tan ⁡ x = sec ⁡ x ,   x ∈ 0,4 π and set B = x :   sin 2 ⁡ x = 1 ,   x ∈ 0,4 π , then

Step-by-step solution

For A ,   sin ⁡ x cos ⁡ x = 1 cos ⁡ x ⇒ sin ⁡ x = 1 ∴   x = π 2 ,   5 π 2 but at x = π 2 ,   5 π 2 tan ⁡ x ,   sec ⁡ θ is not defined ∴   A = ϕ for B ,   sin ⁡ x = 1 ,   sin ⁡ x = - 1 x = π 2 , 5 π 2   or   x = 3 π 2 , 7 π 2 ∴ B = π 2 , 3 π 2 , 5 π 2 , 7 π 2 ∴ n A × B = 0