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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If cot - 1 ⁡ x 2 - 7   cot - 1 ⁡ x + 10 > 0 , then the range of x will be

Options

  1. A( - ∞ , cot ⁡ 2 )
  2. B- ∞ , cot ⁡ 5
  3. Ccot ⁡ 2 , cot ⁡ 5
  4. Dcot ⁡ 2 , ∞

Correct answer

D. cot ⁡ 2 , ∞

Step-by-step solution

cot - 1 ⁡ x - 5 cot - 1 ⁡ x - 2 > 0 ⇒ cot - 1 ⁡ x ∈ - ∞ ,   2 ∪ 5 ,   ∞ ⇒ cot - 1 ⁡ x ∈ 0 ,   2 (Taking intersection with range of cot − 1 x ) ⇒ n ∈ ( cot ⁡ 2 ,   ∞ )

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