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NDA 2016 Maths · Mathematics · Trigonometric Functions and Identities · easy

If tan θ=1/3, then cos 2θ is equal to

Single correct option

If tan⁡θ=13\tan\theta=\dfrac13, then cos⁡2θ\cos2\theta is equal to
  1. A. 35\dfrac35
  2. B. 23\dfrac23
  3. C. 45\dfrac45
  4. D. 12\dfrac12
Show answer and solution

Answer: (C) 45\dfrac45

Use cos⁡2θ=1−tan⁡2θ1+tan⁡2θ=1−1/91+1/9=8/910/9=45\cos2\theta=\dfrac{1-\tan^2\theta}{1+\tan^2\theta}=\dfrac{1-1/9}{1+1/9}=\dfrac{8/9}{10/9}=\dfrac45. The value 35\dfrac35 is sin⁡2θ=2tan⁡θ1+tan⁡2θ\sin2\theta=\dfrac{2\tan\theta}{1+\tan^2\theta}, a different double-angle formula.
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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