If cos - 1 ⁡ x - x 2 2 + x 3 4 - … + sin - 1 ⁡ x 2 - x 4 2 + x 6 4 - … = π 2 for 0 x 2 , then x is equal to

Question

If cos - 1 ⁡ x - x 2 2 + x 3 4 - … + sin - 1 ⁡ x 2 - x 4 2 + x 6 4 - … = π 2 for 0 x 2 , then x is equal to,

MARKS App · Accepted Answer

Since, sin - 1 ⁡ x + cos - 1 ⁡ x = π 2 for x ≤ 1 . ∴ x - x 2 2 + x 3 4 - … = x 2 - x 4 2 + x 6 4 - … ⇒ x 1 + x 2 = x 2 1 + x 2 2 0 x 2 ⇒ x 2 + x = x 2 2 + x 2 ⇒ 2 x + x 3 = 2 x 2 + x 3 ⇒ x 2 = x ⇒ x = 0 , 1 But x 2 = x ≠ 0 , ∴ x = 1 .

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