The differential equation for which `sin^(-1) x + sin^(-1) y = c` is given by

Options

A. `sqrt(1-x^2)dx+sqrt(1-y^2)-dx=0`
B. `sqrt(1-x^2)dy+sqrt(1-y^2)-dx=0`
C. `sqrt(1-x^2)dy-sqrt(1-y^2)-dx=0`
D. `sqrt(1-x^2)dx-sqrt(1-y^2)-dx=0`

Answer

B

Explanation

Given , `sin^(-1)x+sin^(-1)y=c`
`rArr (1)/(sqrt(1-x^2))+(1)/(sqrt(1-y^2))(dy)/(dx)=0`
`rArr sqrt(1-x^2)dy+sqrt(1-y^2)dx=0`
Which is required differential equation .