Find the general solution of the differential equations `sec^2xtany dx+sec^2ytanx dy=0`

Explanation

`sec^(2)xtanydx+sec^(2)ytanxdy=0`
`implies (sec^(2)x)/(tanx)dx+(sec^(2)y)/(tany)dy=0`
`implies int(sec^(2)x)/(tanx)dx+int(sec^(2)y)/(tany)dy=c_(1)`
Le `tanx=timpliessec^(2)xdx=dt` and `tany=zimpliessec^(2)ydy=dz` (where `c_(1)=logc`)
`implies int(1)/(t)dt+int(1)/(z)dz=c_(1)`
`implies logt+logz=logc`
`implies t*z=c`
`implies tanx*tany=c`