find domain

domain according to me shud be only {-1,1 }

cos(sinx) ≥ 0 , for all sinx ,

bcz, cos\theta ≥ 0

for 2n\pi +\frac{\pi }{2}\;\geq \theta \geq 2n\pi - \frac{\pi }{2}
for n = 0 ,

\frac{\pi }{2}\;\geq \theta \geq - \frac{\pi }{2}

i.e,1.57\;\geq \theta \geq-1.57\;\;\;(approx)

and clearly , sinx satisfies the conditions of \theta

since , 1\geq sinx\geq -1

and sin^{-1}(\frac{1+x^{2}}{2x})

is defined only for x = -1, 1

hence the ans