How do you show that the equations are equal?

(tan^2(x))/csc(x) + 1 = tan^4(x)*(csc(x)-1)

How do you show that the equations are equal?

(tan^2(x))/csc(x) + 1 = tan^4(x)*(csc(x)-1)

Actually as writtem these are not equal - because you left out a set of parentheses. I think what you want to show is:

tan^2(x)/(csc(x) + 1) = tan^4(x)*(csc(x)-1)

Start by multiplying both sides by csc(x)+1. You will end up with a term of the form csc^2x-1 on the right side, which can be simplified to 1/tan^2x.