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Ncert Solutions Maths class 11th Maths Class 11th Functions

Let f(x) = $c o s (2 t a n^{- 1} s i n (c o t^{- 1} \sqrt[]{\frac{1 - x}{x}})), 0 < x < 1 . T h e n :$

Option 1 -

${(1 - x)}^{2} f' (x) + 2 {(f (x))}^{2} = 0$

Option 2 -

${(1 - x)}^{2} f' (x) - 2 {(f (x))}^{2} = 0$

Option 3 -

${(1 + x)}^{2} f' (x) + 2 {(f (x))}^{2} = 0$

Option 4 -

${(1 + x)}^{2} f' (x) - 2 {(f (x))}^{2} = 0$

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$f (x) = \frac{1 - x}{1 + x}, 0 < x < 1$ (on simplification)

$f' (x) = \frac{- 2}{{(1 + x)}^{2}}$

${(1 - x)}^{2} f' (x) = - 2 {(f (x))}^{2}$

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Let f(x) = $c o s (2 t a n^{- 1} s i n (c o t^{- 1} \sqrt[]{\frac{1 - x}{x}})), 0 < x < 1 . T h e n :$

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Let f(x) = c o s ( 2 t a n − 1 s i n ( c o t − 1 1 − x x ) ) , 0 < x < 1 . T h e n :

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Let f(x) = $c o s (2 t a n^{- 1} s i n (c o t^{- 1} \sqrt[]{\frac{1 - x}{x}})), 0 < x < 1 . T h e n :$