Question
simplify the expression.
tan(π/2-x)tanx
tan(π/2-x)tanx
Answers
tony
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
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
Steve
works for me.
the <b>co</b>-functions are the functions of the <b>co</b>mplementary angles. So, by definition, tan(π/2-x) = cot(x). Your proof works as well, though.
the <b>co</b>-functions are the functions of the <b>co</b>mplementary angles. So, by definition, tan(π/2-x) = cot(x). Your proof works as well, though.