Derivative of s i n - 1 t 1 + t 2 with respect to c o s - 1 1 1 + t 2 is

Step-by-step solution

Let y = s i n - 1 t 1 + t 2 Put t = t a n θ ⇒ θ = t a n - 1 t = s i n - 1 t a n θ 1 + t a n 2 θ = s i n - 1 t a n θ s e c θ = s i n - 1 s i n θ = θ = t a n - 1 t and z = c o s - 1 1 1 + t 2 = c o s - 1 1 1 + t a n 2 θ = c o s - 1 c o s θ = θ = t a n - 1 t ∴ d y d z = d y d t d z d t = 1 1 + t 2 1 1 + t 2 = 1