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If $S i n^{- 1} (x - \frac{x^{2}}{2} + \frac{x^{3}}{4} - ...) + C o s^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} - ...) = \frac{π}{2}$ for $0 < | x | < \sqrt{2}$ then x=

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Correct option is B

We have sin-1x-x22+x34-.....+cos-1x2-x42+x64-.....=π2 ⇒x-x22+x34-.....=x2-x42+x64-..... ⇒x1+x2=x21+x22 ⇒12+x=x2+x2 ⇒2+x2=2x+x2 ⇒x=1

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If Sin−1x−x22+x34−...+Cos−1x2−x42+x64−...=π2for 0<|x|<2 then x=

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Ready to Test Your Skills?

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If $S i n^{- 1} (x - \frac{x^{2}}{2} + \frac{x^{3}}{4} - ...) + C o s^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} - ...) = \frac{π}{2}$ for $0 < | x | < \sqrt{2}$ then x=