PrepRung
Sign inSign up free

NDA 2016 Maths · Mathematics · Trigonometric Equations · easy

The general solution of tan x=√3 is

Single correct option

The general solution of tan⁡x=3\tan x=\sqrt3 is
  1. A. x=nπ+π3x=n\pi+\dfrac\pi3, n∈Zn\in\mathbb Z
  2. B. x=2nπ+π3x=2n\pi+\dfrac\pi3, n∈Zn\in\mathbb Z
  3. C. x=nπ±π3x=n\pi\pm\dfrac\pi3, n∈Zn\in\mathbb Z
  4. D. x=nπ+π6x=n\pi+\dfrac\pi6, n∈Zn\in\mathbb Z
Show answer and solution

Answer: (A) x=nπ+π3x=n\pi+\dfrac\pi3, n∈Zn\in\mathbb Z

The tangent has period π\pi and tan⁡π3=3\tan\dfrac\pi3=\sqrt3, so x=nπ+π3x=n\pi+\dfrac\pi3. The form 2nπ±α2n\pi\pm\alpha belongs to cosine, and nπ±αn\pi\pm\alpha belongs to sin⁡2\sin^2 or cos⁡2\cos^2 equations; π/6\pi/6 gives 1/31/\sqrt3.
Report a mistake

Original question written in the NDA 2016 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