SOLUTION: please help solve: (cot(x)/csc(x)+1)=(csc(x)-1/cot(x))

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Question 234320: please help solve: (cot(x)/csc(x)+1)=(csc(x)-1/cot(x))
Found 2 solutions by Alan3354, monika_p:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(cot(x)/csc(x)+1)=(csc(x)-1/cot(x))
Is the left side DEN csc? or csc + 1?

Answer by monika_p(71) About Me  (Show Source):
You can put this solution on YOUR website!
cot%28x%29%2F%28csc%28x%29%2B1%29=%28csc%28x%29-1%29%2Fcot%28x%29
cross multiply :
cot%5E2%28x%29=%28csc%28x%29-1%29%2A%28csc%28x%29%2B1%29
use formula %28a-b%29%2A%28a%2Bb%29=a%5E2-b%5E2:
cot%5E2%28x%29=csc%5E2%28x%29-1
substitute csc(x)= 1/sin(x)
cot(x)=cos(x)/sin(x):
%28cos%5E2%28x%29%2Fsin%5E2%28x%29%29=%28%281%2Fsin%5E2%28x%29%29-1%29
multiply both sides by sin^2(x)
cos%5E2%28x%29=1-sin%5E2%28x%29
sin%5E2%28x%29%2Bcos%5E2%28x%29=1 <---- Pythagorean trigonometric identity