CBSE (Commerce) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Differentiate Sin − 1 ( 1 − X 2 1 + X 2 ) + Sec − 1 ( 1 + X 2 1 − X 2 ) , X ∈ R ? - CBSE (Commerce) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Differentiate \[\sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + \sec^{- 1} \left( \frac{1 + x^2}{1 - x^2} \right), x \in R\] ?

Solution

\[\text{ Let, y} = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + se c^{- 1} \left( \frac{1 + x^2}{1 - x^2} \right)\]

\[ \Rightarrow y = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) \left[ Since, se c^{- 1} x = \cos^{- 1} \left( \frac{1}{x} \right) \right]\]

\[ \Rightarrow y = \frac{\pi}{2} \left[ \text{ Since }, \sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2} \right]\]

Differentiate it with respect to x,

\[\therefore \frac{d y}{d x} = 0\] 

  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

Solution for question: Differentiate Sin − 1 ( 1 − X 2 1 + X 2 ) + Sec − 1 ( 1 + X 2 1 − X 2 ) , X ∈ R ? concept: Simple Problems on Applications of Derivatives. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
S
View in app×