solve the equation `cot^-1 x + tan^-1 3 = pi/2`

Explanation

To solve the equation \( \cot^{-1} x + \tan^{-1} 3 = \frac{\pi}{2} \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:

\[ \cot^{-1} x + \tan^{-1} 3 = \frac{\pi}{2} \]

### Step 2: Isolate \( \cot^{-1} x \)
We can isolate \( \cot^{-1} x \) by subtracting \( \tan^{-1} 3 \) from both sides:

\[ \cot^{-1} x = \frac{\pi}{2} - \tan^{-1} 3 \]

### Step 3: Use the cotangent identity
Using the identity that \( \cot^{-1} a + \tan^{-1} a = \frac{\pi}{2} \), we can rewrite the right side:

\[ \cot^{-1} x = \cot^{-1} 3 \]

### Step 4: Set the arguments equal
Since the cotangent function is one-to-one, we can set the arguments equal to each other:

\[ x = 3 \]

### Step 5: Conclusion
Thus, the solution to the equation is:

\[ \boxed{3} \]

---