If tan `alpha = sqrt(3) ` and tan `beta = (1)/(sqrt(3))` , then find the value of cot `(alpha + beta)` .

Answer

To find the value of cot(α + β) given that tan(α) = √3 and tan(β) = 1/√3, we can follow these steps:

### Step 1: Determine the angles α and β
From the given values:
- tan(α) = √3 corresponds to α = 60° (since tan(60°) = √3).
- tan(β) = 1/√3 corresponds to β = 30° (since tan(30°) = 1/√3).

### Step 2: Calculate α + β
Now, we can find α + β:
- α + β = 60° + 30° = 90°.

### Step 3: Find cot(α + β)
We need to find cot(α + β):
- cot(α + β) = cot(90°).

### Step 4: Evaluate cot(90°)
The cotangent of 90° is:
- cot(90°) = 0.

### Final Answer
Thus, the value of cot(α + β) is 0.

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