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99 Percentile Qs Bank for JEE MainMathematicsInverse Trigonometric Functions

Let f x = cosec - 1 1 + sin 2 x , where · denotes the greatest integer function. Then f x equals;

Options

  1. Aπ 2
  2. Bπ 2 , cosec - 1 2
  3. Ccosec - 1 2
  4. DNone of these

Correct answer

B. π 2 , cosec - 1 2

Step-by-step solution

Given, f x = cosec - 1 1 + sin 2 x , where · denotes the greatest integer function. Since, - 1 ≤ sin x ≤ 1 ⇒ 0 ≤ sin 2 x ≤ 1 ⇒ 1 ≤ 1 + sin 2 x ≤ 2 ⇒ 1 + sin 2 x = 1 ,   1 ≤ sin 2 x < 2 and 1 + sin 2 x = 2 ,   if    2 ≤ 1 +   sin 2 x < 3 . So, f x = cosec - 1 1 ⇒ f x = π 2 And, f x = cosec - 1 2 ⇒ f x = cosec - 1 2 Therefore, f x has two values π 2 , cosec - 1 2  

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