Answer:
True 
Step-by-step explanation:
assuming that you meant to write 
cot (x-π//2) = - tan x 
the identity is TRUE because,
- you can graph cot (x-π//2)  and  - tan x,  and see that the graphs overlap
OR
-you solve for cot (x-π/2) 
useful to know is that : 
cot x=1/tan x, tan x = sin x/cos x,  
cos(x) =cos(-x), sin(-x) = -sin x, 
cos(π/2 -x) =sin x, sin (π/2-x) =cos x
cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x
cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1 
cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x),  use facts: cos(x) =cos(-x), sin(-x) = -sin x
cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x
cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x
cot (x-π/2) = -tan x