Solve for `x` : `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: Rearrange the equation
Start by isolating \( \cot^{-1} x \):
\[ \cot^{-1} x = \frac{\pi}{2} - \tan^{-1} 3 \]

### Step 2: Apply the cotangent function
Now, take the cotangent of both sides:
\[ \cot(\cot^{-1} x) = \cot\left(\frac{\pi}{2} - \tan^{-1} 3\right) \]

### Step 3: Use the cotangent identity
Using the identity \( \cot\left(\frac{\pi}{2} - \theta\right) = \tan(\theta) \), we can rewrite the right side:
\[ x = \tan(\tan^{-1} 3) \]

### Step 4: Simplify using the tangent identity
Using the identity \( \tan(\tan^{-1} \theta) = \theta \):
\[ x = 3 \]

### Final Answer
Thus, the solution for \( x \) is:
\[ \boxed{3} \]

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