How do you verify $cot(x - pi/2) = -tan(x)$ ?

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Answer 1 · 2016-10-07T20:33:40

see below

$cot(x-pi/2)=-tanx$

Left Side : $=cot(x-pi/2)$

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

$=(cosxcos(pi/2)+sinxsin(pi/2))/(sinxcos(pi/2)-cosxsin(pi/2)$

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

$=sinx/-cosx$

$=-tanx$

$:.=$ Right Side

How do you verify cot(x - pi/2) = -tan(x)cot(x - pi/2) = -tan(x)?