Asked by tony
                simplify the expression.
tan(π/2-x)tanx
            
        tan(π/2-x)tanx
Answers
                    Answered by
            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
                    Answered by
            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.
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