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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Trigonometric Equations

NDA 2014 · Mathematics · Trigonometric Equations

The complete solution of 3 ^2 x=1 is given by:

The complete solution of 3tan⁡2x=13 \tan ^2 x=1 is given by:

Options

  1. Ax=nπ±π3x=n \pi \pm \frac{\pi}{3}
  2. Bx=nπ+π3x=n \pi+\frac{\pi}{3} only
  3. Cx=nπ±π6x=n \pi \pm \frac{\pi}{6}
  4. Dx=nπ+π6x=n \pi+\frac{\pi}{6} only where n∈Zn \in \mathbb{Z}

Correct answer

C. x=nπ±π6x=n \pi \pm \frac{\pi}{6}

Step-by-step solution

⇒3tan⁡2x=1⇒tan⁡2x=13tan⁡x=±13=±tan⁡π6⇒x=nπ±π6.\begin{array}{rlrl}\Rightarrow \quad 3 \tan ^2 x & =1 \\ \Rightarrow \quad \tan ^2 x & =\frac{1}{3} \\ \tan x & = \pm \frac{1}{\sqrt{3}}= \pm \tan \frac{\pi}{6} \\ \Rightarrow \quad & & x & =n \pi \pm \frac{\pi}{6}.\end{array}
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