Prove that `sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1`

Explanation

To prove that \( \sin^{-1}(\cos(\sin^{-1}(x))) + \cos^{-1}(x) = \frac{\pi}{2} \) for \( |x| \leq 1 \), we will break the proof into two cases based on the value of \( x \).

### Step 1: Consider the case when \( 0 \leq x \leq 1 \)

1. **Evaluate \( \sin^{-1}(x) \)**:
Let \( \theta = \sin^{-1}(x) \). Then, by definition, \( \sin(\theta) = x \).

2. **Find \( \cos(\theta) \)**:
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