Is cosx/sinx the same ast cotx nd how

well cotx as you should know is 1/tanx

and tanx = sinx/cosx

so if u invert both sides (as in flip both of them up side down) u get

1/tanx=cosx/sinx

therefor:
cotx=cosx/sinx

Yes, by the definition of cotangent. Also, "ast" is not the same as "as" and "nd" is not the same as "and".

cot x = (cos x) / (sin x)

cot x = adjacent / opposite

cos x = adjacent / hypotenuse

sin x = opposite / hypotenuse

cos x / sin x = [adjacent / hypotenuse] / [opposite / hypotenuse] = adjacent / opposite

qed

tan = sin/cos

cot = 1/tan = 1/ sin/cos = cos/sin