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

Answers (1)

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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