Question

How do you simplify `cos(x-y)/sin(x+y)-4cot(x+y)` to trigonometric functions of x and y?

Answer 1

It is

#cos(x-y)/sin(x+y)-4cot(x+y)=[cos(x-y)]/[sin(x+y)]-4cot(x+y)= [cosx*cosy+sinx*siny]/[sinx*cosy+cosx*siny]-4*[cos(x+y)]/[sin(x+y)]= [cosx*cosy+sinx*siny]/[sinx*cosy+cosx*siny]-4*[cosx*cosy-sinx*siny]/[sinx*cosy+cosx*siny)= [-3cosx*cosy+5sinx*siny]/[sinx*cosy+cosx*siny]#