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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main · Mathematics · Inverse Trigonometric Functions

If& f(x) = ^ - 1 (cosec( ^ - 1 x)) + ^ - 1 ( ( ^ - 1 x)), ~then~ f...

If& f(x)=sin⁡−1(cosec(sin⁡−1x))+cos⁡−1(sec⁡(cos⁡−1x)),f\left(x\right) = \sin^{- 1}\left(cosec\left(\sin^{- 1}x\right)\right) + \cos^{- 1}\left(\sec \left(\cos^{- 1}x\right)\right),~then~f(x)f ( x )& takes:

Options

  1. Aexactly two values
  2. Bone value
  3. Cundefined
  4. Dinfinite values

Correct answer

B. one value

Step-by-step solution

<blockquote><p>Giventhat:<blockquote><p>Given that:f\left(x\right) = \sin^{- 1} \left(cosec \left(\sin^{- 1}x\right)\right) + \cos^{- 1}\lleft(\sec \left(\cos^{- 1}x\right))</p><p>Clearly</p><p>Clearlyf ( x )isdefinedonlyfor is defined only for~x = \pm1 and ~and~f\left(1\right) = f\left(-1\right) = \dfrac{π}{2}</p><p>So,bothvaluesgivethesameresult.Therefore,ithasonlyone and valuetotake.</p></blockquote></p><p>So, both values give the same result. Therefore, it has only one \text{ and } value to take.</p></blockquote>
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