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Let f (x) = log e (sinx ), ( 0 lt x lt p...

Let `f (x) = log _e (sinx ), ( 0 lt x lt pi ) and g(x) = sin ^(-1) (e ^(-x)), (x ge 0)`. If `alpha` is a positive real number such that ` a = ( fog)' ( alpha ) and b = (fog ) ( alpha )`, then (A) `aalpha ^(2) - b alpha - a = 0` (B) `a alpha ^(2) - b alpha - a = 1 ` (C) `a alpha ^(2) + b alpha - a = - 2 alpha ^(2)` (D) `a alpha ^(2) + b alpha + a = 0`

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