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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The value of ( ^ -1 x) is

The value of sin⁡(cot⁡−1x)is\sin \left(\cot^{-1} x\right) is

Options

  1. A1+x2\sqrt{1 + x^{2}}
  2. Bxx
  3. C11+x2\dfrac{1}{\sqrt{1 + x^{2}}}
  4. D1−x2\sqrt{1 - x^{2}}

Correct answer

C. 11+x2\dfrac{1}{\sqrt{1 + x^{2}}}

Step-by-step solution

Let,& cot⁡−1x=A,(cot⁡2A)=x2\cot^{- 1} \text{x} = \text{A} , \left(\cot^{2} A\right) = x^{2}

1+(cot⁡2A)=1+x2=cosec2A1 + \left(\cot^{2} A\right) = 1 + x^{2} = cosec^{2}A

\dfrac{1}{\sin^{2 } \text{A}} = 1 + x^{2} ⇒ \text\sin\text{A} = 1 / \sqrt{1 + x^{2}}

⇒ \text\sin \left(\cot^{-1 } \text{x}\right) = 1 / \sqrt{1 + x^{2}}
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