trig
posted by tony .
simplify the expression.
tan(π/2x)tanx

tan (pi/2  x) = sin (pi/2  x) / cos (pi/2  x)
But sin (pi/2  x) = cos x
and
cos (pi/2  x) = sin x
<=>
tan (pi/2  x) = cos x / sin x = cotan x
<=>
tan (pi/2  x) * tan x =
cotan x * tan x =
(cos x / sin x) * (sin x / cos x) =
1 
works for me.
the cofunctions are the functions of the complementary angles. So, by definition, tan(π/2x) = cot(x). Your proof works as well, though.