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NDA 2019 Maths · Mathematics · Trigonometric Equations · medium

How many angles x with 0≤ x<2π satisfy 2cos ^2x+3sin x=3?

Single correct option

How many angles xx with 0≤x<2π0\le x<2\pi satisfy 2cos⁡2x+3sin⁡x=32\cos^2x+3\sin x=3?
  1. A. 22
  2. B. 44
  3. C. 55
  4. D. 33
Show answer and solution

Answer: (D) 33

Replace cos⁡2x=1−sin⁡2x\cos^2x=1-\sin^2x: 2sin⁡2x−3sin⁡x+1=02\sin^2x-3\sin x+1=0, so sin⁡x=1\sin x=1 or sin⁡x=12\sin x=\frac12. This gives x=π2x=\frac\pi2, π6\frac\pi6, 5π6\frac{5\pi}6: 33 solutions. Forgetting that sin⁡x=12\sin x=\frac12 has two roots in the interval gives 22.
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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