Question

Verify that fxy= fyx , when f is equal to sin-1(y/x)​

Answer 1

Step-by-step explanation:

For solution refer to Annexure

Answer 2

Given:

f is equal to sin-1/(y/x)

To Find

fxy= fyx

Solution:

sin-1 y/x- sin-1 x/y= sin-1               ($\frac{y}{x} \frac{\sqrt{y^{2}-x^{2} } }{y} - \frac{x}{y} {\sqrt{x^{2} -}y^{2} } /x$)

= $\frac{\sqrt{} y^{2}-x^{2} }{x} -$ √x²-y²/y

now, y²- x² and x²- y² should be positive it is only possible when bot are 0.

⇒ sin-1$\frac{y}{x}$ - sin-1$\frac{x}{y}$ = 0

⇒ fxy = fyx

Hence, proved that fxy= fyx.