SOLUTION: if f(x) = {{{(1+x)/(1-x)}}} show that f(f(tan(<font face = "symbol">q</font>))) = -cot(<font face = "symbol">q</font>) ( this question is taken from 11th standard maths text chapte

Algebra ->  Trigonometry-basics -> SOLUTION: if f(x) = {{{(1+x)/(1-x)}}} show that f(f(tan(<font face = "symbol">q</font>))) = -cot(<font face = "symbol">q</font>) ( this question is taken from 11th standard maths text chapte      Log On


   

Question 639049: if f(x) = %281%2Bx%29%2F%281-x%29 show that f(f(tan(q))) = -cot(q) ( this question is taken from 11th standard maths text chapter trigonometry / functions , q refers to angle)
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = %281%2Bx%29%2F%281-x%29

The trick is to get f(f(x)) and simplify it BEFORE 
you substitute tan(q)

f(f(x)) = 

Multiply top and bottom by LCD of (1-x)

f(f(x)) = %28%281-x%29%2B%281%2Bx%29%29%2F%28%281-x%29-%281%2Bx%29%29


f(f(x)) = %281-x%2B1%2Bx%29%2F%281-x-1-x%29

f(f(x)) = 2%2F%28-2x%29

f(f(x)) = cross%282%29%2F%28-cross%282%29x%29

f(f(x)) = -1%2Fx

Now substitute x = tan(q)

f(f(tan(q))) = -1%2Ftan%28theta%29

f(f(tan(q))) = -cot(q)

Edwin