Question

verify the identity cot(x-pi/2)=-tanx

Answer 1

$\cot(x-\frac{\pi}{2}) = \dfrac{\cos(x-\frac{\pi}{2})}{\sin(x-\frac{\pi}{2})} =\dfrac{\cos(-(\frac{\pi}{2}-x))}{\sin(-(\frac{\pi}{2}-x))} =\dfrac{\cos(\frac{\pi}{2}-x)}{-\sin(\frac{\pi}{2}-x)} =\\=-\dfrac{\sin x}{\cos x} = -\tan x$