If `y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)),0ltxlt1,` prove that`(dy)/ (dx)="4/(1+x^2)`

Explanation

To prove that \(\frac{dy}{dx} = \frac{4}{1+x^2}\) for the given function \(y = \sin^{-1}\left(\frac{2x}{1+x^2}\right) + \sec^{-1}\left(\frac{1+x^2}{1-x^2}\right)\), we will follow these steps:

### Step 1: Substitute \(x = \tan \theta\)
Let \(x = \tan \theta\). Then, we have:
\[ \theta = \tan^{-1}(x) \]
This substitution will help us simplify the expressions involving trigonometric identities.
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