PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for Differentiate Sin − 1 ( 1 − X 2 1 + X 2 ) + Sec − 1 ( 1 + X 2 1 − X 2 ) , X ∈ R ? - PUC Karnataka Science Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### 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?

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Solution 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.
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