SOLUTION: prove that (1/(1+cos x))-(1/(1-cos x))=cosec x cot x

Algebra ->  Trigonometry-basics -> SOLUTION: prove that (1/(1+cos x))-(1/(1-cos x))=cosec x cot x      Log On


   

Question 972937: prove that (1/(1+cos x))-(1/(1-cos x))=cosec x cot x
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the left hand side, and use your already-learned fraction skills (like converting each rational expression to its equivalent with simplest common denominator). Continue from there.

Trying to continue working with the left hand side, you still may want to convert the right hand side to its form in sines and cosines to help in finding how to continue making it into the right hand side.




%281-cos%28x%29-%281%2Bcos%28x%29%29%29%2F%281-cos%5E2%28x%29%29

%28-2cos%28x%29%29%2F%281-cos%5E2%28x%29%29

-2cos%28x%29%2Fsin%5E2%28x%29,
I do not see the left side becoming the right side. The factor negative two throws it off.

You should be able to find the correct adjusted steps if the right-side is actually 2%2Acsc%28x%29cot%28x%29, but this still seems to be wrong in sign.

---

I rechecked this very carefully on paper. The left side becomes -2%2Acsc%28x%29cot%28x%29.