Which expression is equivalent to square root of the fraction with numerator 1 minus cosine of 10 x and denominator 2 end root ?

Use the half-angle identity (1 − cos θ)/2 = sin²(θ/2). With θ = 10x, the square root becomes √(sin²(5x)) = |sin(5x)|, so the intended choice is sine of 5x. Strictly, this equals sine of 5x itself when sin(5x) is nonnegative; otherwise the principal square root gives its absolute value.

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