Question 816236
{{{(1+ cos(2X))/ (sin(2X)) = f(x)}}}
When you learned about the cos(2x) I hope you learned all three variations:<ul><li>cos(2x) = cos^2(x)-sin^2(x)</li><li>cos(2x) = 2cos^2(x)-1</li><li>cos(2x) = 1-2sin^2(x)</li></ul>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:
{{{(1+ (2cos^2(x)-1))/(2sin(x)cos(x)) = f(x)}}}
The +1 and -1 cancel:
{{{2cos^2(x)/(2sin(x)cos(x)) = f(x)}}}
The factors of 2 (in front) will cancel:
{{{cos^2(x)/(sin(x)cos(x)) = f(x)}}}
The cos(x) in the denominator will cancel with one of the two factors of cos(x) in the numerator:
{{{cos(x)/sin(x) = f(x)}}}
which is equal to:
{{{cot(x) = f(x)}}}