How do you prove $Cotx = -tan(x - pi/2)$ ?

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Answer 1 · 2016-05-09T20:50:57

see below

Right Side: $=-tan(x-pi/2)$

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

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

$=-(sinx xx 0-cosx xx 1)/(cos x xx 0+sinx xx 1)$

$=-(-cosx/sinx)$

$=cot x$

How do you prove Cotx = -tan(x - pi/2)Cotx = -tan(x - pi/2)?