simplify the expression.

Question

tan(π/2-x)tanx

Answer 1

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

Answer 2

works for me.

the co-functions are the functions of the complementary angles. So, by definition, tan(π/2-x) = cot(x). Your proof works as well, though.