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  • Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 20 maths

Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 20 maths

Answers (1)

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Answer:

\frac{d y}{d x}=0, \text { for all } x \in R

Hint:

-1<\frac{1-x^{2}}{1+x^{2}} \leq 1 \text { holds for all } x \in R

Given:

y=\sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)+\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)
Solution:  

-1<\frac{1-x^{2}}{1+x^{2}} \leq 1 \text { holds for all } x \in R

So,

y=\sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)+\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)=\frac{\pi}{2} ; \text { for all } x \in R

\therefore \sin ^{-1} m+\cos ^{-1} m=\frac{\pi}{2}, m \in(-1,1)

Hence,

\frac{d y}{d x}=0, \text { for all } x \in R

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