1. **Problem:** Given that $\sin A = \frac{3}{5}$ and $0^\circ \leq A \leq 90^\circ$, find the value of $(\tan A - \cos A)$. 2. **Formula and rules:** Recall the definitions: - $\sin A = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan A = \frac{\sin A}{\cos A}$ Since $\sin A = \frac{3}{5}$, the opposite side is 3 and hypotenuse is 5. Use Pythagoras theorem to find adjacent side: $$\text{adjacent} = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$$ 3. **Calculate $\cos A$ and $\tan A$: $$\cos A = \frac{4}{5}$$ $$\tan A = \frac{\sin A}{\cos A} = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4}$$ 4. **Evaluate $(\tan A - \cos A)$: $$\tan A - \cos A = \frac{3}{4} - \frac{4}{5} = \frac{15}{20} - \frac{16}{20} = -\frac{1}{20}$$ 5. **Answer:** The value of $(\tan A - \cos A)$ is $-\frac{1}{20}$, which corresponds to option A.