Concept:Use the standard identity sin−1x+cos−1x=2π to simplify the given angle.Explanation:Let E=cos(2cos−1x+sin−1x).Write 2cos−1x as cos−1x+cos−1x.Then E=cos[(sin−1x+cos−1x)+cos−1x].Using sin−1x+cos−1x=2π, we get:E=cos(2π+cos−1x)Apply the identity cos(2π+θ)=−sinθ:E=−sin(cos−1x)Let θ=cos−1x. Then cosθ=x and in the principal range, sinθ=1−x2.So E=−1−x2.Substitute x=51:E=−1−251=−2524=−526Answer:−526 (Option C)