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NDA 2019 Maths · Mathematics · Inverse Trigonometric Functions · medium

The value of cos (2sin ^-11/3) is

Single correct option

The value of cos⁡(2sin⁡−113)\cos\left(2\sin^{-1}\dfrac13\right) is
  1. A. 19\dfrac19
  2. B. 223\dfrac{2\sqrt2}3
  3. C. 79\dfrac79
  4. D. 59\dfrac59
Show answer and solution

Answer: (C) 79\dfrac79

Let θ=sin⁡−113\theta=\sin^{-1}\frac13. Then cos⁡2θ=1−2sin⁡2θ=1−29=79\cos2\theta=1-2\sin^2\theta=1-\frac29=\frac79. Option 223\frac{2\sqrt2}{3} is cos⁡θ\cos\theta, and 19\frac19 comes from using sin⁡2θ\sin^2\theta alone.
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Original question written in the NDA 2019 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