Question

If $tan\theta =\sqrt{n}$ for some non-square natural number n, then sec2$\theta$ is

• A. A rational number
• B. An rational number
• C. A positive number a θ
• D. A positive integer a θ

Answer 1

The correct option is A

A rational number

sec2$\theta$ = $\frac{1+ta{n}^2\theta }{1-ta{n}^2\theta }=\frac{1+n}{1-n}$

Where n is a non-square natural number

So, 1 - n $\ne$ 0

$\Rightarrow sec2\theta$ is a rational number.