Notice that you didn't include enough parentheses in the way you
typed the problem.  You had THIS:

cot^2 x/csc x+1 = 1 - sin x/ sin x

When you have to type mathematics all on one line, there must be 
enough parentheses to tell where numerators and denominators start 
and end.  You should have typed THIS instead:

cot^2(x)/[csc(x)+1] = [1 - sin(x)]/sin(x)

The way you typed it, there is no way to tell whether the 1's are
part of the denominator on the left and the numerator on the right
or whether they are separate terms.  So learn to be careful to use
enough parentheses when typing mathematics all on one line.  I was
able to tell that you meant because you used the word "quantity".



Use the identity  solved for  
to substitute in the left side for .



Factor the numerator as the difference of two squares:



Cancel:





Use the identity 



Write 1 as 



Get LCD by multiplying  by 







Edwin