Concept:Use the identity sin−1x+cos−1x=2π and the cosine addition formula.Explanation:Given expression: cos(2cos−1x+sin−1x).Rewrite the angle as (sin−1x+cos−1x)+cos−1x.Using sin−1x+cos−1x=2π, the expression becomes cos(2π+cos−1x).Apply cos(2π+θ)=−sinθ, so we get −sin(cos−1x).Let θ=cos−1x. Since 0≤θ≤π, sinθ=1−x2.Therefore, the value is −1−x2.Substitute x=51:−1−(51)2=−1−251=−2524.Answer:−2524Option A.