Read the following information and answer the two items that follow : 

Let $\frac{\tan \left(3\mathrm{A}\right)}{\tan \left(\mathrm{A}\right)} = \mathrm{k}$ where tan A ≠ 0 and $\mathrm{K} \ne \frac{1}{3}$

For real values of tan A, K cannot lie between

• $\frac{1}{3} \mathrm{and} 3$

• $\frac{1}{2} \mathrm{and} 2$

• $\frac{1}{5} \mathrm{and} 5$

• $\frac{1}{7} \mathrm{and} 7$

Read the following information and answer the two items that follow :Let $\frac{\tan \left(3\mathrm{A}\right)}{\tan \left(\mathrm{A}\right)} = \mathrm{K},$ where tan A ≠ 0 and $\mathrm{K} = \frac{1}{3}$

What is tan²(A) equal to ? 

• $\frac{\mathrm{K} + 1}{3\mathrm{K} + 1}$

• $\frac{\mathrm{K} - 1}{3\mathrm{K} - 1}$

• $\frac{3\mathrm{K} - 1}{\mathrm{K} - 1}$

• $\frac{\mathrm{k} + 3}{3\mathrm{k} - 1}$