Question

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

Answer 1

see below

Explanation:

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`