Solve the following inequality:
`cos^(-1)xlt2`

Explanation

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

### Step 1: Understand the function
The function \( \cos^{-1} x \) (or arccosine of \( x \)) is defined for \( x \) in the interval \([-1, 1]\). The output of \( \cos^{-1} x \) is in the range \([0, \pi]\).

### Step 2: Set up the inequality
We need to find the values of \( x \) such that:
\[ \cos^{-1} x < 2 \]

### Step 3: Solve the inequality
To solve for \( x \), we first need to find the value of \( x \) when \( \cos^{-1} x = 2 \):
\[ x = \cos(2) \]

### Step 4: Calculate \( \cos(2) \)
Using a calculator or trigonometric tables, we find:
\[ \cos(2) \approx -0.416 \]

### Step 5: Determine the interval
Since \( \cos^{-1} x \) is less than 2, we need to find the values of \( x \) such that:
\[ x > \cos(2) \approx -0.416 \]

### Step 6: Consider the domain of \( \cos^{-1} x \)
The function \( \cos^{-1} x \) is only defined for \( x \) in the interval \([-1, 1]\). Therefore, we combine the results:
\[ -0.416 < x \leq 1 \]

### Final Solution
Thus, the solution to the inequality \( \cos^{-1} x < 2 \) is:
\[ x \in (-0.416, 1] \]