Question

If tanθ = $\sqrt{n}$ for some non-square natural number n, then

sec2θ is

• A. A rational number
• B. An irrational number
• C. A positive number
• D. None of these

Answer 1

Answer: (A)

A rational number

Answer 2

$\sec 2\theta = \frac{1 + \tan^{2}\theta}{1 - \tan^{2}\theta} = \frac{1 + n}{1 - n}$

where n is a non-square natural number so that 1 – n ≠ 0.

⇒ sec2θ is a negative rational number