If sin^{-1} (x- x^2/4 + x^3/4 .......) + cos^{-1} (x^2 - x^4/2 + x^6/4......) = π/2 for 0 < |x| < √2, then x equals ​

Question

If \(sin^{-1} (x- \frac{x^2}2 + \frac{x^3}4....) + cos^{-1} (x^2 - \frac{x^4}{2} + \frac{x^6}4.......) = \frac \pi2\) for 0 < |x| < √2, then x equals

(a) 1/2

(b) 1

(c) – 1/2

(d) –1

Answer 1

Correct option is (b) 1