SOLUTION: Verify Cos(theta) / (1+cos(theta)) + cos(theta)/(1-cos(theta)) = 2 cot(theta) csc(theta)

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Question 938561: Verify
Cos(theta) / (1+cos(theta)) + cos(theta)/(1-cos(theta)) = 2 cot(theta) csc(theta)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that:

%22%22=%22%22+2cot%28theta%29csc%28theta%29

Start with the left side, get LCD and combine fractions.
You can use the rule A%2FB%2BC%2FD=%28AD-CB%29%2F%28BD%29



Factor cos%28theta%29 out of the top:
Multiply the bottom out like (a+b)(a-b)=a2-b2



Simplify the top. The bottom is just sin2(q)

 

Simplify the top some more:

++%28cos%28theta%29%282%29%29%2F%0D%0Asin%5E2%28theta%29

++%282cos%28theta%29%29%2F%0D%0Asin%5E2%28theta%29

That's as simple as we can get the left side in terms of sines and 
cosines. Let's start with the other side and get it down as simple 
as possible in terms of sines and cosines.  It is permissible to
work with the other side to get it to the same expression.  So we
start with the other side:

2cot%28theta%29csc%28theta%29

2%28cos%28theta%29%2Fsin%28theta%29%29%281%2Fsin%28theta%29%29

Immediately that is the same as

++%282cos%28theta%29%29%2F%0D%0Asin%5E2%28theta%29

[Note: If you're worried about working with both sides, all you
have to do is reverse those last three steps and tack them on to the
first part, and then you will have only worked with the left side.]

Edwin