Now separating variable x on one side and variable y on another side, we have,

– cot(x) dx = sec²y cot(y) dy

Integrating both sides we get,

Sin2x = 2 sinx cosx

Using identities:

and

– log| sinx | = log| tany |+ c

Using: log(a)+log(b) = log(ab)

log( sin x tan y) = log c

sin(x) tan(y) = c