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Trigonometric Functions · Class 11 · CBSE · Science Mathematics

How many solutions does the equation 2sin²x − 3sin x + 1 = 0 have in the interval [0, 2π]?

Practice question from Trigonometric Functions (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-10AF1C

How many solutions does the equation 2sin²x − 3sin x + 1 = 0 have in the interval [0, 2π]?

  1. A.1
  2. B.2
  3. C.3Correct answer
  4. D.4

Solution

Let y=sin⁡xy=\sin x. Then 2y2−3y+1=02y^2-3y+1=0, so (2y−1)(y−1)=0(2y-1)(y-1)=0 and hence sin⁡x=1/2\sin x=1/2 or sin⁡x=1\sin x=1. In [0,2π][0,2\pi], these give x=π/6,5π/6,π/2x=\pi/6,5\pi/6,\pi/2, respectively, so there are 3 solutions.

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