Question 396589
Verify following is an identity.
(1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1) 

Starting with the right hand side,                      notes:

(cot^2(x))/(csc(x)-1) =(cos^2/sin^2)/((1/sin)-1)
                      =(cos^2/sin^2)/(1-sin)/sin)
                      =(cos^2/sin^2)*(sin/(1-sin)) (invert and multiply)
                      =(cos^2/(sin)(1-sin)
                      =(1-sin^2)/(sin)(1-sin)      (difference of 2 squares)
                      =(1+sin)(1-sin)/(sin)(1-sin) ((1-sin) cancels out)
                      =(1+sin)/sin

 ans:  right hand side=left hand side