Let A,B,C be the three angles such that `A+B+C=pi , tan A.tan B=2`, then find the value of `(cos A cos B)/(cos C)`

Explanation

To solve the problem step by step, we will start with the given information and use trigonometric identities to find the required value.

### Step 1: Understand the given information
We are given that \( A + B + C = \pi \) and \( \tan A \tan B = 2 \). We need to find the value of \( \frac{\cos A \cos B}{\cos C} \).

**Hint:** Recall that if \( A + B + C = \pi \), then \( C = \pi - (A + B) \).

### Step 2: Express \( C \) in terms of \( A \) and \( B \)
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