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NDA 2023 Maths · Mathematics · Trigonometric Equations · medium

The number of values of x in the interval [0,2π] satisfying |cos x|=1/2 is

Single correct option

The number of values of xx in the interval [0,2π][0,2\pi] satisfying ∣cos⁡x∣=12|\cos x|=\dfrac12 is
  1. A. 2
  2. B. 3
  3. C. 4
  4. D. 6
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Answer: (C) 4

∣cos⁡x∣=12|\cos x|=\frac12 means cos⁡x=12\cos x=\frac12 or cos⁡x=−12\cos x=-\frac12. Each has two solutions in [0,2π][0,2\pi]: π3,5π3\frac\pi3,\frac{5\pi}3 and 2π3,4π3\frac{2\pi}3,\frac{4\pi}3. Total 44. Counting only cos⁡x=12\cos x=\frac12 gives the trap value 22.
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