If ^ -1 (x - x^2 2 + x^3 4 - ) + ^ -1 (x^2 - x^4 2 + x^6 4 - ) = 2 for 0 < |x| < 2 then x equals

JEE Advanced Mathematics question

If for then equals

Answer: (B)

Both series are geometric (ratios and , of modulus since ):

A = x - + = = , B = - + = = .

Sin

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Question ID VK-110568