Question

If $\tan \theta =\sqrt{n}$ for some rational number n, then $\sec 2\theta$ is-

• A. A rational number
• B. An irrational number
• C. A positive number
• D. Any real numbers

Answer 1

Answer: (A)

A rational number

$\sec 2\theta =\frac{1+{\tan }^2\theta }{1-{\tan }^2\theta }=\frac{1+n}{1-n}$
This is a rational number.Hence option A is correct