Question

Verify the identity.

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

Answer 1

\(\sin(x-\frac{\pi}{2})=-\cos(x)\)

and

\(\cos(x-\frac{\pi}{2})= \sin(x)\)

Answer 2

what am i suppose to do with those?

Answer 3

\[\cot (x-\frac {\pi}{2})=\frac{\cos (x-\frac{\pi}{2})}{\sin (x-\frac{\pi}{2})}=\frac{\cos x \cos \frac{\pi}{2}+\sin x \sin \frac{\pi}{2}}{\sin x \cos \frac{\pi}{2}-\cos x \sin \frac{\pi}{2}}=\]\[\frac{\cos x(0)+\sin x(1)}{\sin x(0)-\cos x(1)}=\frac{\sin x}{-\cos x}=- \tan x\]

Answer 4

thats all?

Answer 5

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

Answer 6

@lxoser