need to factor tanx - sec^x / tanx down (ans. is -cotx)

[airika713]

i have to factor this problem down:

tanx - sec^2x/tanx

and i know the answer is -cotx because i checked in the back of the book but ive tried everything and cannot figure out how to get that. please help.

 

[Loren]

tanx - sec^2x/tanx means \(\displaystyle \tan x-\frac{\sec^2 x}{\tan x}\) and I don't think that simplifies to -cot x.