The correct option is B Only one real number
cos{sin−113+cos−1x}=0
⇒sin−113+cos−1x=(2n−1)π2,n ϵ Z
⇒sin−1x=(2n+1)π2−sin−113
⇒sin−1x=(2n+1)π2−sin−113
⇒0≤(2n+1)π2−sin−113≤π,n ϵ Z
⇒n=0 ⇒cos−1x=π2−sin−113=cos−113
⇒x=13
∴ Solution set has only one real number.