1) If tan θ = √n for some non-square natural number n, then sec 2θ is : A) a rational number B) an irrational number C) a positive number D) none of the above Answer: Option AExplanation:$\cos2\theta =\frac{1-\tan^{2}\theta}{1+\tan^{2}\theta}$ = $\frac{1-n}{1+n}$→ $\sec2\theta =\frac{1+n}{1-n}$ Since, n is non - square natural number, n ≠ 1 .'. $\sec2\theta =\frac{1+n}{1-n}$ = rational number
