Answer:
f(b)=(b-b^2)/(1+b^2),
f(tan x)=[tan(x)-tan^2(x)]/[cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)]
=[tan(x)-tan^2(x)]/[1/cos^2(x)]
=[tan(x)-tan^2(x)]*cos^2(x)
=[sin(x)/cos(x)-sin^2(x)/cos^2(x)]*cos^2(x)
=sin(x)cos(x)-sin^2(x) or =1/2*sin2x+1/2*cos2x-1/2
