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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.4 Question 3 Subquestion (ii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.4 Question 3 Subquestion (ii) Maths Textbook Solution.

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Answer:  \left ( -\infty,-1 \right ] \cup \left [ 1,\infty\right )
Hint: Domain of  \sec ^{-1}\left ( x \right ) is \:\left ( -\infty,-1\right ] \cup \left [ 1,\infty \right )
           Domain of  \tan ^{-1}\left ( x \right ) is R
Given: \sec ^{-1}\left ( x \right )-\tan ^{-1}x
Solution:We know that the domain of   \sec ^{-1}\left ( x \right ) is \left ( -\infty,1 \right ]\cup \left [ 1,\infty \right ) \cdot \cdot \cdot \cdot \cdot (i)
                   Domain of  \tan ^{-1}x\: is \: R \cdot \cdot \cdot \cdot \cdot \cdot (ii)
Union of (i) and (ii) will be domain of the given function
\left ( -\infty,-1 \right ] \cup \left [ 1,\infty\right )\cup R
\Rightarrow \left ( -\infty,-1 \right ] \cup \left [ 1,\infty\right )
The domain of the given function is \left ( -\infty,-1 \right ] \cup \left [ 1,\infty\right ).

 

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