For 0 is less than x comma x is less than pi over 2 , which expression is equivalent to the fraction with numerator sine open paren x over 2 close paren and denominator 1 minus cosine of x ?

Use the half-angle identity sin(x/2) = √((1 − cos x)/2). Since 0 < x < π/2, sin(x/2) is positive, so substituting and simplifying gives sin(x/2)/(1 − cos x) = 1/√(2(1 − cos x)). This matches choice A, whose denominator is √(2(1 − cos x)).

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