Question:

The number of solutions of the equation tan x + sec x = 2 cos x and cos x ≠ lying in the interval (0, 2π) is

Updated On: Apr 27, 2024
  • (A) 2
  • (B) 1
  • (C) 0
  • (D) 3
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The Correct Option is D

Solution and Explanation

Explanation:
tan⁡x+sec⁡x=2cos⁡x1+sin⁡x=2−2sin2⁡x2sin2⁡x+sin⁡x−1=0(2sin⁡x−1)(sin⁡x+1)=0sin⁡x=−1,12Therefore, number of solutions in (0,2π)=3
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