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If y = ((sin^ (−1) x)) , prove that...

If `y = `((sin^ (−1)` x)) ` `, prove that ( 1 − x^ 2 ) d 2 y d x 2 − x d y d x = 0

A

x+y

B

1+xy

C

1-xy

D

xy-2

Text Solution

Verified by Experts

`y=(sin^(-1))/(sqrt(1-x^(2)))`
`therefore" "(dy)/(dx)=(sqrt(1-x^(2))(1)/(sqrt(1-x^(2)))-(sin^(-1)x)(1)/(2)((-2x))/(sqrt(1-x^(2))))/(1-x^(2))`
`"or "(1-x^(2))(dy)/(dx)=1+x((sin^(-1)x)/(sqrt(1-x^(2))))=1+xy`
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