The problem asks to find the value of $cosA$ given that $sinA = \frac{3}{8}$ and $tanA = \frac{3}{4}$.

1. Problem Description

The problem asks to find the value of $cosA$ given that $sinA = \frac{3}{8}$ and $tanA = \frac{3}{4}$.

2. Solution Steps

We are given $sinA = \frac{3}{8}$ and $tanA = \frac{3}{4}$.

We know that $tanA = \frac{sinA}{cosA}$.

Therefore, $cosA = \frac{sinA}{tanA}$.

Substituting the given values, we have $cosA = \frac{\frac{3}{8}}{\frac{3}{4}} = \frac{3}{8} \cdot \frac{4}{3} = \frac{12}{24} = \frac{1}{2}$.

3. Final Answer

The value of $cosA$ is $\frac{1}{2}$. The correct option is b.