SOLUTION: (cot)/(csc-1)=(csc+1)/(cot) please prove this for me :)

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Question 467680: (cot)/(csc-1)=(csc+1)/(cot)
please prove this for me :)
Found 2 solutions by Alan3354, lwsshak3:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
(cot)/(csc-1)=(csc+1)/(cot)
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Change all to sines and cosines
(cos/sin)/(1/sin - 1) = (1/sin + 1)/(cos/sin)
(cos/sin)/((1 - sin)/sin) = ((1 + sin)/sin)/(cos/sin)
cos/(1-sin) = (1 + sin)/cos
Cross multiply
cos^2 = 1 - sin^2 Pythagorean identity
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Always change to sines and cosines, unless you're familiar with other identities.

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
(cot)/(csc-1)=(csc+1)/(cot)
...
Left side:
(cos/sin)/((1/sin)-1)
(cos/sin)/(1-sin/sin)
cancel out sin
cos/(1-sin)
multiply by (1+sin)
cos/(1-sin)*(1+sin)/(1+sin)
cos(1+sin)/1-sin^2
cos(1+sin)/cos^2
(1+sin)/cos
1/cos+sin/cos
csc+tan
..
right side:
(csc+1)/(cot)
csc/cot+1/cot
(1/sin)/(cos/sin)+1/cot
1/cos+1/cot
csc+tan
Proof: right side=left side