If `tanA=(3)/(4)`, then show that sin A cos A`=(12)/(25)

Explanation

To solve the problem where we need to show that if \( \tan A = \frac{3}{4} \), then \( \sin A \cos A = \frac{12}{25} \), we can follow these steps:

### Step 1: Understand the definition of tangent
Given that \( \tan A = \frac{3}{4} \), we can interpret this in terms of a right triangle. The tangent of an angle in a right triangle is defined as the ratio of the opposite side (height) to the adjacent side (base).

### Step 2: Draw a right triangle
Let's draw a right triangle where:
- The height (opposite side) = 3
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