The value of tan - 1 ⁡ 1 + x 2 + 1 - x 2 1 + x 2 - 1 - x 2 , x 1 2 , x ≠ 0 , is equal to:

Question

The value of tan - 1 ⁡ 1 + x 2 + 1 - x 2 1 + x 2 - 1 - x 2 , x 1 2 , x ≠ 0 , is equal to:, π 4 + 1 2 cos - 1 ⁡ x 2, π 4 - cos - 1 ⁡ x 2, π 4 - 1 2 cos - 1 ⁡ x 2, π 4 + cos - 1 ⁡ x 2

MARKS App · Accepted Answer

Assume that , x 2 = cos ⁡ 2 θ ; θ = 1 2 cos -1 x 2 ∴ tan - 1 ⁡ 1 + cos ⁡ 2 θ + 1 - cos ⁡ 2 θ 1 + cos ⁡ 2 θ - 1 - cos ⁡ 2 θ = tan - 1 ⁡ 2 cos 2 θ + 2 sin 2 θ 2 cos 2 θ - 2 sin 2 θ = tan - 1 ⁡ cos θ + sin θ cos θ - sin θ = tan - 1 ⁡ 1 + tan ⁡ θ 1 - tan ⁡ θ = tan - 1 ⁡ tan ⁡ π 4 + θ = π 4 + 1 2 cos - 1 ⁡ x 2

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