If `f(x)=(1-x^(2))/(1+x^(2))`, then prove that:
`f(tan theta)=cos 2theta`

(i) If f(x) = x + (1)/(x) prove that: [f(x)]^(3) = f(x^(3)) + 3f ((1)/(x)) (ii) If f(x) = x^(3) - (1)/(x^(3)) , prove that f(x) + f((1)/(x)) = 0 (iii) If f(x) = (1-x^(2))/(1+ x^(2)) , prove that f (tan theta) = cos 2 theta

If f(x)=(1-x^(2))/(1+x^(2)) then show that f(tan theta)=cos2 theta

If f: R to R is defined by f(x)=(1-x^(2))/(1+x^(2)) then show that f(tantheta)=cos2theta.

If f: R to R is defined by f(x)=(1-x^(2))/(1+x^(2)) then show that f(tantheta)=cos2theta.

If f(x) =(1-x^2)/(1+x^2) , prove that f (tan theta)= cos 2 theta .

If f (x)= (2x)/(1+x^2) , prove that f (tan theta)=sin 2 theta .

if f(x)=(1-x)/(1+x) then prove that f(cos2 theta)=tan^(2)theta

If f(x)=(1-x)/(1+x) , then f[ f(cos2 theta)]=

If f (x)= (1+x)/(1-x) , show that f (f (tan theta))=- cot theta .