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If f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(...

If `f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(2))sin^(-1)(1-{x}))/(sqrt(2) ({x} - {x}^(3)))",",x gt 0),(k",",x = 0),((A sin^(-1)(1-{x})cos^(-1)(1-{x}))/(sqrt(2{x})(1-{x}))",",x lt 0):}` is continuous at x = 0, then the value of `sin^(2) k + cos^(2) ((Api)/(sqrt(2)))`, is..... (where {.} denotes fractional part of x).

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