Given, y=sin−1x and z=cos−1(√1−x2) Put x=sin‌θ, we get y=sin−1(sin‌θ) and z=cos−1(√1−sin2θ) ⇒‌‌y=θ‌‌ and ‌‌z=cos−1(cos‌θ) ⇒‌‌y=θ‌‌ and ‌‌z=θ ⇒‌‌y=z On differentiating w.r.t. z, we get ‌