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

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

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

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