PrepRung
Sign inSign up free

NDA 2018 Maths · Mathematics · Trigonometric Equations · medium

How many solutions does tan ^2x=3 have in [0,2π]?

Single correct option

How many solutions does tan⁡2x=3\tan^2x=3 have in [0,2π][0,2\pi]?
  1. A. 2
  2. B. 3
  3. C. 6
  4. D. 4
Show answer and solution

Answer: (D) 4

tan⁡x=±3\tan x=\pm\sqrt3. tan⁡x=3\tan x=\sqrt3 gives π/3,4π/3\pi/3,4\pi/3; tan⁡x=−3\tan x=-\sqrt3 gives 2π/3,5π/32\pi/3,5\pi/3. That makes 4 solutions; taking only the positive root yields the incorrect count 2.
Report a mistake

Original question written in the NDA 2018 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