Solve the differential equation :
`sec^(2)x tan y dx + sec^(2) y tan x dy = 0`

Explanation

Given, differential equation is ,
`sec^(2)x.tany.dx+sec^(2)y.tan x . Dy = 0 `
`:.(sec^(2)x)/(tan x).dx+(sec^(2)y)/(tan y).dy =0`
On integrating both sides, we get
`int (sec^(2)x)/(tan x)dx + int (sec^(2)y)/(tan y).dy=0`
`:.` The general solution is
`log|tan x | + log | tan y | = log c [:'int(f'(x))/(f(x)).dx=log|f(x)|+c]`
`:.log|tan x . tan y | = log c`
`:. tan x . tan y = c `