Question

Verify the identity.

cot ( x - pi/2 ) = -tan x

Answer 1

Medal and fan rewarded!

Answer 2

Can you help please? @hartnn or anyone?

Answer 3

You can use a graph for this problem or the sum formula for angles. I will use the latest,
\[\sin(x-\pi/2)=\sin x\cos(\pi/2)-\cos x\sin(\pi/2)=-\cos x\\
\cos(x-\pi/2)=\cos x\cos(\pi/2)+\sin x\sin(\pi/2)=\sin x\\
\cot(x-\pi/2)=\frac{1}{\sin (x-\pi/2)/\cos (x-\pi/2)}=\frac{1}{-\cos x/\sin x}=-\tan x\]