Mathematics | VITEEE 2019 | Discussion Page

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

Option A

$\cos2\theta =\frac{1-\tan^{2}\theta}{1+\tan^{2}\theta}$

= $\frac{1-n}{1+n}$ → $\sec2\theta =\frac{1+n}{1-n}$

Since, n is non - square natural number, n ≠ 1

.'. $\sec2\theta =\frac{1+n}{1-n}$ = rational number

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