If the trigonometric equation tan - 1 ⁡ x = 2 sin - 1 ⁡ a has a solution, then the complete set of values of a is

Question

If the trigonometric equation tan - 1 ⁡ x = 2 sin - 1 ⁡ a has a solution, then the complete set of values of a is, 1 2 a 1 2, all real values of a, a 1 2, a 1 2

MARKS App · Accepted Answer

∵ tan - 1 ⁡ x ∈ - π 2 , π 2 ∴ - π 2 2 sin - 1 ⁡ a π 2 - π 4 sin - 1 ⁡ a π 4 ⇒ a ∈ - 1 2 , 1 2

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