PrepRung
Sign inSign up free

NDA 2019 Maths · Mathematics · Trigonometric Functions and Identities · medium

The value of tan (π)/(8) is

Single correct option

The value of tan⁡π8\tan\dfrac\pi8 is
  1. A. 2+1\sqrt2+1
  2. B. 2−1\sqrt2-1
  3. C. 2−12\dfrac{\sqrt2-1}{2}
  4. D. 2−22-\sqrt2
Show answer and solution

Answer: (B) 2−1\sqrt2-1

Use tan⁡θ2=1−cos⁡θsin⁡θ\tan\dfrac\theta2=\dfrac{1-\cos\theta}{\sin\theta} with θ=π4\theta=\dfrac\pi4: 1−1212=2−1≈0.414\dfrac{1-\frac{1}{\sqrt2}}{\frac1{\sqrt2}}=\sqrt2-1\approx0.414. Since π8=22.5∘\dfrac\pi8=22.5^\circ is less than 45∘45^\circ, the tangent must be less than 11, which rejects 2+1\sqrt2+1, the value of tan⁡3π8\tan\dfrac{3\pi}8.
Report a mistake

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake