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If $S i n^{- 1} (x - \frac{x^{2}}{2} + \frac{x^{3}}{4} .....) + \cos^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} ....) = \frac{π}{2}$ 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-.... ⇒x=x2 ⇒xx-1=0 ⇒x=0,1 Since 0

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IfSin−1x−x22+x34.....+cos−1x2−x42+x64....=π2for0<x<2 thenx=

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Ready to Test Your Skills?

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