Find the value of `sin^(-1)(2^x)` (ii) `cos^(-1)sqrt(x^2-x+1)` `tan^(-1)(x^2)/(1+x^2)` (iv) `sec^(-1)(x+1/x)`

Explanation

Let's solve each part of the question step by step.

### Part (i): Find the value of \( \sin^{-1}(2^x) \)

1. **Identify the domain**: The function \( \sin^{-1}(y) \) is defined for \( y \) in the range \([-1, 1]\). Therefore, we need to find the values of \( x \) for which \( 2^x \) lies within this range.

\[
-1 \leq 2^x \leq 1
...