Verified answer

well, hello from France !

"and it goes like this..."

f(x) = (1-x)(tan(πx/2))

we will use the result :

lim (a ----> 0) tan(a)/a = 1

so

let be : e = 1 - x, we then have :

(1-x)(tan(πx/2)) = e tan( (π/2)(1 - e) )

= e tan( π/2 - πe/2)

= e / tan(πe/2)

= (2/π) (πe/2) / tan(πe/2) ------> 2 / π

so for a = πe/2 ----> 0 when e -----> 0 (when x > 1)

lim ( x -----> 1 of ) (1-x)(tan(πx/2)) = 2 / π

et voilà, Mademoiselle !

hope it' ll help !!