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.Com
Question 639049: if f(x) = 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)   (Show Source): You can put this solution on YOUR website!
f(x) = 

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)) = 


f(f(x)) = 

f(f(x)) = 

f(f(x)) = 

f(f(x)) = 

Now substitute x = tan(q)

f(f(tan(q))) = 

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

Edwin
RELATED QUESTIONS

If cotq = -3/4 and sinq < 0,... (answered by AnlytcPhil)

I am confused on these type of problems, please help. 
If f(x)=x(x+3)(x-1),... (answered by Edwin McCravy)

Find the minimum value of cosq + 2sin (answered by Edwin McCravy)

 how do you Verify this equation?: sin(np +  (answered by Edwin McCravy)



Prove that this equation is an identity:
                        (answered by uma,Edwin McCravy)

Show that the equation below is NOT an identity.

Ö (answered by Edwin McCravy)

This is a trignometry problem on proving identities
I can use:double-angle,sum and... (answered by Edwin McCravy)

Find the exact value of sin(2q) if csc( (answered by stanbon,Edwin McCravy)

For what numbers q, 0≦ (answered by Edwin McCravy)