Posted by **tony** on Sunday, July 14, 2013 at 8:48pm.

simplify the expression.

tan(π/2-x)tanx

- trig -
**tony**, Sunday, July 14, 2013 at 8:57pm
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

- trig -
**Steve**, Monday, July 15, 2013 at 4:56am
works for me.

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

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