Solve `cos^(-1)x >cos^(-1)x^2`

Explanation

To solve the inequality \( \cos^{-1}x > \cos^{-1}x^2 \), we can follow these steps:

### Step 1: Understand the properties of the inverse cosine function
The function \( \cos^{-1}x \) is a decreasing function in the interval \( [-1, 1] \). This means that if \( a < b \), then \( \cos^{-1}a > \cos^{-1}b \).

### Step 2: Set up the inequality
Given the inequality \( \cos^{-1}x > \cos^{-1}x^2 \), we can use the property of the decreasing function. This implies that we need to have:
\[
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