Question

could someone please tell me what the other angle identity of tan is? Thank you much!

"...other angle identity of tan x"?

in relation to which "other" ?

there are many identities dealing with the tangent.
The most important is probably

tan x = sin x/cos x

The Pythagorean Relationship would be

tan^2 x + 1 = sec^2 x

how about tan(2A) = 2tan A/(1-tan^2 A)

yes, i do know those, thank you. but my teacher told us that there is a specific identity for "the other angle". for example, the other angle identity of sinx = cos90-x. I believe the "other angle" identity for tanx is cot90-x but i'm not sure.

yes, you are right, tanx = cot(90-x)

if you are ever unsure about an identity like that pick an obscure angle such as 78.4º and test it with your calculator
tan 78.4 = 4.87162
cot(90-78.4)=cot 11.6º = 1/tan 11.6 = 4.87162