SOLUTION: Proof cos(2x)/(1 + sin(2x)) = (cot(x) - 1)/(cot(x) + 1) Restrictions: Can't use creative one's or cross multiply, only Trig functions

Algebra ->  Trigonometry-basics -> SOLUTION: Proof cos(2x)/(1 + sin(2x)) = (cot(x) - 1)/(cot(x) + 1) Restrictions: Can't use creative one's or cross multiply, only Trig functions      Log On


   

Question 1072868: Proof
cos(2x)/(1 + sin(2x)) = (cot(x) - 1)/(cot(x) + 1)
Restrictions: Can't use creative one's or cross multiply, only Trig functions
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Identities to use starting with the left side, but start at the Right Hand Side:

cos%282x%29=cos%5E2%28x%29-sin%5E2%28x%29=2cos%5E2%28x%29-1
---
sin%282x%29=2sin%28x%29cos%28x%29


Keeping those two identities in mind, begin with the RightHandSide of the ID to be proved.

%28%28cos%28x%29%2Fsin%28x%29%29-1%29%2F%28%28cos%28x%29%2Fsin%28x%29%29%2B1%29

.
%28cos%28x%29-sin%28x%29%29%2F%28cos%28x%29%2Bsin%28x%29%29





%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%282sin%28x%29cos%28x%29%2B1%29, used the basic pythagorean identity

Using the two identities listed above,
cos%282x%29%2F%28sin%282x%29%2B1%29
.