Question

if y=tan^-1*(x-1)+a*tan(pi/8), where 'a' is a real constant, find the minimum value of 'a' for which y>0 for all x

Answer 1

tan^-1(x-1) is bounded by -Pi/2<=tan^-1(x-1)<=Pi/2
so if you whant y>0 for all x, it must be bigger than Pi/2. So :
a*tan(pi/8)>pi/2
and
a>(pi/2)/(tan(pi/8))