If x ∈ 0 , 1 , then the value of 2 tan - 1 ⁡ 1 - x 2 2 x + 2 cos - 1 ⁡ 1 - x 2 1 + x 2 is equal to

Question

If x ∈ 0 , 1 , then the value of 2 tan - 1 ⁡ 1 - x 2 2 x + 2 cos - 1 ⁡ 1 - x 2 1 + x 2 is equal to, - π 2, 0, π 2, π

MARKS App · Accepted Answer

∴ Let y = 2 tan - 1 ⁡ 1 - x 2 2 x + 2 cos - 1 ⁡ 1 - x 2 1 + x 2 Putting x = tan ⁡ θ As, x ∈ 0,1 , θ ∈ 0 , π 4 and π 2 - 2 θ ∈ 0 , π 2 ∴ y = 2 tan - 1 ⁡ cot ⁡ 2 θ + 2 cos - 1 ⁡ cos ⁡ 2 θ = 2 tan - 1 ⁡ tan ⁡ π 2 - 2 θ + 2 cos - 1 ⁡ cos ⁡ 2 θ = 2 π 2 - 2 θ + 4 θ = π

Search any question & find its solution

Looking for more such questions to practice?