If `sin^(-1) (x^(2) + 2x + 2) + tan^(-1) (x^(2) - 3x - k^(2)) gt (pi)/(2)`, then find the value of k

Explanation

To solve the inequality \( \sin^{-1}(x^2 + 2x + 2) + \tan^{-1}(x^2 - 3x - k^2) > \frac{\pi}{2} \), we will follow these steps:

### Step 1: Rewrite the Inequality
We start with the given inequality:
\[ \sin^{-1}(x^2 + 2x + 2) + \tan^{-1}(x^2 - 3x - k^2) > \frac{\pi}{2} \]

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