If `sec^(-1)((x+y)/(x-y))=a^(2)`, show that `(dy)/(dx)=(y)/(x)`.

Explanation

Given `sec^(-1)((x+y)/(x-y))=a^(2)`
`=(x+y)/(x-y)=sec(a^(2))=b("say")`
`impliesx+y=b(x-y)`
`impliesx+y=bx-by`
`impliesy(1+b)=(b-1)x`
`impliesy=((b-1)/(1+b))x`
`impliesy=cx" where "c=(b-1)/(1+b)=(y)/(x)" "......(i)`
Differentianting w.r.t.x,
`(dy)/(dx)=c(y)/(x)y=cx" "`[From (i)]
`:.(dy)/(dx)=(y)/(x)`