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

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

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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