Q1 / 83 · NTA Abhyas (JEE Main) 2020 · Mathematics · Trigonometric Equations

If the expression (1+tan⁡x+tan2⁡x)(1-cot⁡x+cot2⁡x) is positive, then the complete set of values of x is

  • A
    0,π2
  • B
    0,π
  • Correct answer
    C
    R- x=nπ2, n∈I
  • D
    0, ∞

Solution

(1+tan⁡x+tan2⁡x)(1+tan2x-tan⁡x)tan2⁡x>0

⇒ 1+tan2⁡x2-tan2⁡xtan2⁡x>0

Since, 1+tan2⁡x>tan2⁡x, ∀x ∈R-x=nπ2, n∈I

Hence, given expression is positive for all values of x ∈R-x=nπ2, n∈I

Hence, the correct answer is option: 'C'.

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