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If sec((x+y)/(x-y))=a^(2),"then "(d^(2)y...

If `sec((x+y)/(x-y))=a^(2),"then "(d^(2)y)/(dx^(2))=......`

A

y

B

x

C

`(y)/(x)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`sec((x+y)/(x-y))=a^(2)`
`rArr" "(x+y)/(x-y)=sec^(-1)(a^(2))`
Differentiating w.r.t. x, we get
`(x-y)(1+(dy)/(dx))-(x+y)(1-(dy)/(dx))=0`
`rArr" "x=y+(x-y)(dy)/(dx)-x-y+(x+y)(dy)/(dx)=0`
`rArr (dy)/(dx)(x-y+x+y)=2y`
`rArr (dy)/(dx)=(2y)/(2x)`
`rArr (dy)/(dx)=(y)/(x)`
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