Question

The value of $\tan^{2}(\sec^{-1}(3))$ is

• A. 8
• B. 4
• C. 6
• D. 1
• E. 10

Hint:

Logic Tip: You can also solve this by sketching a right triangle. If $\sec\theta = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{3}{1}$, then by Pythagorean theorem, the opposite side is $\sqrt{3^2 - 1^2} = \sqrt{8}$. Thus, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{8}}{1}$, and $\tan^2\theta = 8$.

Answer 1

The Correct Option is A