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If , where a, x ∈ (0, 1) then, the value of x is

We are given that,

Where, a, x ∈ (0, 1).

We need to find the value of x.

Using property of inverse trigonometry,

Then, we can write as

⇒ 2 tan^-1 a + 2 tan^-1 a = 2 tan^-1 x

⇒ 4 tan^-1 a = 2 tan^-1 x

Dividing both sides by 2,

⇒ 2 tan^-1a = tan^-1 x

Using property of inverse trigonometry,

Then,

Taking tangent on both sides,

Or,