The relation tan - 1 ⁡ 1 + x 1 - x = π 4 + tan - 1 ⁡ x holds true for all

Question

The relation tan - 1 ⁡ 1 + x 1 - x = π 4 + tan - 1 ⁡ x holds true for all, x ∈ R, x ∈ ( - ∞ , 1 ), x ∈ ( - 1 , ∞ ), x ∈ ( - ∞ , 2 )

MARKS App · Accepted Answer

Given, tan - 1 ⁡ 1 + x 1 - x = π 4 + tan - 1 ⁡ x RHS = π 4 + tan - 1 ⁡ x = tan - 1 ⁡ 1 + tan - 1 ⁡ x = tan - 1 ⁡ 1 + x 1 - x , if x 1 ∴ x ∈ ( - ∞ , 1 )

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