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

Question

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, B ⊂ A, A = B, A ∩ B = B, n A × B = 0

MARKS App · Accepted Answer

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

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