How do you verify the identity $cot(pi/2-x)=tanx$ ?

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Answer 1 · 2017-02-06T18:38:42

see below

Left Hand Side:

$cot(pi/2 -x)=cos(pi/2 -x)/sin(pi/2 -x)$

Use the formulas $cos(A-B)=cosAcosB+sinAsinB$ and
$sin(A-B)=sinAcosB-cosAsinB$

$=(cos (pi/2)cosx+sin(pi/2)sinx)/(sin(pi/2)cosx-cos(pi/2)sinx$

$=(0*cosx+1*sinx)/(1*cosx-0*sinx)$

$=sinx/cosx$

$=tanx$

$:. =$ Right Hand Side

How do you verify the identity cot(pi/2-x)=tanxcot(pi/2-x)=tanx?