How do you verify #cot(x)/sin(x)-tan(x)/cos(x)=csc(x)sec(x)1/(sin(x)+cos(x))# ?

I've got this headache of a trig identity. Any advice is appreciated!

#cot(x)/sin(x)-tan(x)/cos(x)=csc(x)sec(x)1/(sin(x)+cos(x))#