If the median of a triangle through A is perpendicular to AB, then

Options

A. 2tanA+tanB=0
B. 2tanA-tanB=0
C. tanA-2tanB=0
D. tanA+2tanB=0

Explanation

To solve the problem, we need to analyze the given triangle \( ABC \) where the median from vertex \( A \) to side \( BC \) is perpendicular to \( AB \). Let's denote the midpoint of \( BC \) as \( D \).

### Step-by-Step Solution:

1. **Draw Triangle and Identify Points**:
- Draw triangle \( ABC \) with points \( A \), \( B \), and \( C \).
- Mark the midpoint \( D \) of side \( BC \).

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