Question

If $z={\sec }^{-1}\left(\frac{x^4+y^4-8x^2{y}^2}{x^2+y^2}\right)$ then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=$

• A. $\cot z$
• B. $2\cot z$
• C. $2\tan z$
• D. $\sec z$

Answer 1

Answer: (B)

$2\cot z$

$\sec z=\frac{x^4+y^4-8^2{y}^2}{x^2+y^2}$
sec z is a hom ageneous of degree=2
$\sum x\frac{d\sec z}{dx}=n\sec z$
$\sec z\tan z(\sum \frac{xdz}{dx})=n\sec z$

$(\sum \frac{xdz}{dx})=2\cot z$