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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The value of sin ⁡ cot - 1 ⁡ x is

Options

  1. A1 + x 2
  2. Bx
  3. C1 1 + x 2
  4. D1 - x 2

Correct answer

C. 1 1 + x 2

Step-by-step solution

Let, cot − 1 x = A , cot 2 ⁡ A = x 2 1 + cot 2 ⁡ A = 1 + x 2 = c o s e c 2 A 1 sin 2 A = 1 + x 2 ⇒ sin A = 1 / 1 + x 2 ⇒ sin cot -1 x = 1 / 1 + x 2

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