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The number of real solution of the equat...

The number of real solution of the equation
`sin^(-1) (underset(i=1)overset(oo)sum x^(i +1) -x underset(i=1)overset(oo)sum ((x)/(2))^(i))`
`= (pi)/(2) - cos^(-1) (underset(i=1)overset(oo)sum (-(x)/(2))^(i) - underset(i=1)overset(oo)sum (-x)^(i))` lying in the interval `(-(1)/(2), (1)/(2))` is ______.
(Here, the inverse trigonometric function `sin^(-1) x and cos^(-1) x` assume values in `[-(pi)/(2), (pi)/(2)] and [0, pi]` respectively)

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The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

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