Answer:
-cot(x)
Explanation:
tanx-(sec^2x / tanx)
Lets get a common denominator of tan
tan x * tan x/ tan -sec ^2 x/ tan x
tan ^2 x - sec ^2 x
---------------------------
tan x
We know than sec^2 - tan^2 =1 (trig identity) so factor out -1
-1(-tan ^2 x + sec ^2 x)
---------------------------
tan x
-1(1)
---------------------------
tan x
-1
----------
tan (x)
We know 1/ tan x = cot (x)
- cot(x)