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Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  19

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Answer: 0

Hint: \cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2}

Given: y=\sec ^{-1}\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)+\sin ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)

Solution:

 y=\cos ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)+\sin ^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)

    \begin{aligned} &=\frac{\pi}{2} \\\\ &=0 \end{aligned}

 

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