How do you prove Cotx = -tan(x - pi/2)cotx=tan(xπ2)?

1 Answer
May 9, 2016

see below

Explanation:

Right Side:=-tan(x-pi/2)=tan(xπ2)

=-sin(x-pi/2)/cos(x-pi/2)=sin(xπ2)cos(xπ2)

=(-sinx cos(pi/2)-cos x sin (pi/2))/((cosxcos(pi/2))+sinx sin (pi/2))=sinxcos(π2)cosxsin(π2)(cosxcos(π2))+sinxsin(π2)

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

=-(-cosx/sinx)=(cosxsinx)

=cot x=cotx