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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If the trigonometric equation tan - 1 ⁡ x = 2 sin - 1 ⁡ a has a solution, then the complete set of values of a is

Options

  1. A1 2 < a < 1 2
  2. Ball real values of a
  3. Ca < 1 2
  4. Da < 1 2

Correct answer

D. a < 1 2

Step-by-step solution

&#8757; tan - 1 &#8289; x &#8712; - &#960; 2 , &#960; 2 &#8756; - &#960; 2 &#60; 2 sin - 1 &#8289; a &#60; &#960; 2 - &#960; 4 &#60; sin - 1 &#8289; a &#60; &#960; 4 &#8658; a &#8712; - 1 2 , 1 2

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