# If tanθ = √n , for some non-square natural number n , then sec2θ is

Q: If tanθ = √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

Sol. $\large sec2\theta = \frac{1 + tan^2\theta}{1- tan^2 \theta}= \frac{1+n}{1-n}$

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

⇒ sec2θ is a rational number.

Hence (A) is the correct answer.