SOLUTION: Simplify (sinx/1-cosx) + (1-cosx/sinx) Thanks in advance!

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Question 1059837: Simplify
(sinx/1-cosx) + (1-cosx/sinx)
Thanks in advance!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What do you really have? Put the grouping symbols where they need to be.

%28sin%28x%29%2F%281-cos%28x%29%29%29%2B%28%281-cos%28x%29%29%2Fsin%28x%29%29
OR
%28sin%28x%29%2F%281-cos%28x%29%29%29%2B%281-cos%28x%29%2Fsin%28x%29%29
?

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.

Write the fractions with the common denominator. Then simplify using sin%5E2%28x%29+%2B+cos%5E2%28x%29 = 1. Then cancel the common factors. 

  %28sin%28x%29%2F%281-cos%28x%29%29%29%2B%28%281-cos%28x%29%29%2Fsin%28x%29%29 = 


=  = 


=  = 


= %282-2cos%28x%29%29%2F%28sin%28x%29%2A%281-cos%28x%29%29%29 = %282%2A%281-cos%28x%29%29%29%2F%28sin%28x%29%2A%281-cos%28x%29%29%29 = %282%2Across%281-cos%28x%29%29%29%2F%28sin%28x%29%2Across%281-cos%28x%29%29%29 = 


= 2%2Fsin%28x%29 = 2*cosec(x).


To see more solved similar problems on proving trigonometry identities look into the lesson
    - Proving Trigonometry identities
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Trigonometry: Solved problems".