If sin - 1 x + tan - 1 x = π / 2 , then 2 x 2 + 1 =

Question

If sin - 1 x + tan - 1 x = π / 2 , then 2 x 2 + 1 =, 5, 5 - 1 2, 2, 5 + 1 2

MARKS App · Accepted Answer

We have, sin - 1 x + tan - 1 x = π 2 ⇒ 0 x 1 ∴ tan - 1 x = π 2 - sin - 1 x = cos - 1 x ⇒ tan - 1 x = tan - 1 1 - x 2 x ⇒ x 2 = 1 - x 2 ⇒ x 4 + x 2 - 1 = 0 ⇒ x 2 = - 1 ± 5 2 as x 2 > 0 ∴ x 2 = 5 - 1 2 ⇒ 2 x 2 + 1 = 5

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