The x satisfying sin-1x+sin-1(1-x)=cos-1xare

sin−1(1−x)=π2−sin−1x−sin−1x ∵cos−1x=π2−sin−1xsin−1(1−x)=π2−2sin−1x ⇒1−x=sinπ2−2sin−1x=cos2sin−1x=cos2θ, where sin−1x=θ⇒1−x=1−2sin2θ=1−2x2 or x(1−2x)=0 or x=0,12