Write sin-1( x+ square root 1-x2/ root 2 in the simplest form 

Let y = sin-1x+1-x22y = sin-112×x + 12×1-x2y = sin-1sinπ4×x + cosπ4×1-x2Let x = cos αThen sin α = 1-cos2α = 1-x2Now, y = sin-1sinπ4 × cos α + cosπ4×sinαy = sin-1sinπ4+αy = π4+αy = π4+cos-1x

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