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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The set x ∈ ℝ: 2x + 2 ^ 2 x = 2 is equal to

The set {x \in \mathbb{R}: \cos 2x + 2\cos^{2} x = 2 }is equal to

Options

  1. A{2nπ+π3:n∈Z}\left\{2n\pi + \dfrac{\pi}{3}: n \in Z\right\}
  2. B{nπ±π6:n∈Z}\left\{n\pi \pm \dfrac{\pi}{6}: n \in Z\right\}
  3. C{nπ+π3:n∈Z}\left\{n\pi + \dfrac{\pi}{3}: n \in Z\right\}
  4. D{2nπ−π3:n∈Z}\left\{2n\pi - \dfrac{\pi}{3}: n \in Z\right\}

Correct answer

B. {nπ±π6:n∈Z}\left\{n\pi \pm \dfrac{\pi}{6}: n \in Z\right\}

Step-by-step solution

Given, 2cos⁡2x−1+2cos⁡2x=22\cos^{2} x - 1 + 2\cos^{2} x = 2

⇒cos⁡2x=34⇒ \cos^{2} x = \dfrac{3}{4}

cos⁡2x=cos⁡2π6\cos^{2} x = \cos^{2} \dfrac{π}{6}

∴x=nπ±π6:n∈Z∴ x = n\pi \pm \dfrac{\pi}{6}: n \in \mathbb{Z}
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