SOLUTION: Find the function that will make the given equation an identity: (1+ cos(2X))/ (sin(2X)) = f(x)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the function that will make the given equation an identity: (1+ cos(2X))/ (sin(2X)) = f(x)      Log On


   

Question 816236: Find the function that will make the given equation an identity:
(1+ cos(2X))/ (sin(2X)) = f(x)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2B+cos%282X%29%29%2F+%28sin%282X%29%29+=+f%28x%29
When you learned about the cos(2x) I hope you learned all three variations:
  • cos(2x) = cos^2(x)-sin^2(x)
  • cos(2x) = 2cos^2(x)-1
  • cos(2x) = 1-2sin^2(x)
While all of them will work in this problem, the one in the middle, with the -1, will work well in our numerator with its +1:
%281%2B+%282cos%5E2%28x%29-1%29%29%2F%282sin%28x%29cos%28x%29%29+=+f%28x%29
The +1 and -1 cancel:
2cos%5E2%28x%29%2F%282sin%28x%29cos%28x%29%29+=+f%28x%29
The factors of 2 (in front) will cancel:
cos%5E2%28x%29%2F%28sin%28x%29cos%28x%29%29+=+f%28x%29
The cos(x) in the denominator will cancel with one of the two factors of cos(x) in the numerator:
cos%28x%29%2Fsin%28x%29+=+f%28x%29
which is equal to:
cot%28x%29+=+f%28x%29