if sec(x+y/x-y)=a^2 show that dy/dx = y/x - Maths - Limits and Derivatives

Question

if sec(x+y/x-y)=a^2
show that dy/dx = y/x

Chetna Khanna · Accepted Answer

$\sec (\frac{x + y}{x - y}) = a^{2}$

Differentiating both the sides, with respect to x

$\sec (\frac{x + y}{x - y}) \tan (\frac{x + y}{x - y}) {\frac{(x - y) (1 + \frac{d y}{d x}) - (x + y) (1 - \frac{d y}{d x})}{(x - y)^{2}}} = 0 A s \sec (\frac{x + y}{x - y}) \neq 0 \tan (\frac{x + y}{x - y}) \neq 0 ∴ {\frac{(x - y) (1 + \frac{d y}{d x}) - (x + y) (1 - \frac{d y}{d x})}{(x - y)^{2}}} = 0 \Rightarrow (2 x \frac{d y}{d x} - 2 y) = 0 \Rightarrow \frac{d y}{d x} = \frac{y}{x}$