Question 140847
{{{(cos(x) - cos(y))/(sin(x) + sin(y)) + (sin(x) - sin(y))/(cos(x) + cos(y)) = 0}}}


LCD is just the product of the denominators, so:
{{{(((cos(x) - cos(y))(cos(x)+cos(y))) + ((sin(x) - sin(y))(sin(x)+sin(y))))/((sin(x)+sin(y))(cos(x) + cos(y))) = 0}}}


{{{(cos^2(x)-cos^2(y)+sin^2(x)-sin^2(y))/((sin(x)+sin(y))(cos(x) + cos(y)))=0}}} (Difference of 2 squares)


{{{(cos^2(x)+sin^2(x)-cos^2(y)-sin^2(y))/((sin(x)+sin(y))(cos(x) + cos(y)))=0}}}


{{{(cos^2(x)+sin^2(x)-(cos^2(y)+sin^2(y)))/((sin(x)+sin(y))(cos(x) + cos(y)))=0}}}


{{{(1-1)/((sin(x)+sin(y))(cos(x) + cos(y)))=0}}} (because {{{cos^2(alpha)+sin^2(alpha)=1}}})


{{{0/((sin(x)+sin(y))(cos(x) + cos(y)))=0}}}