tan x - cot x
I like to rewrite in terms of sin and cos
sin x/ cos x - cos x/ sin x
Get a common denominator
sin x/ cos x * sin x / sin x - cos x / sin * cos x / cos x
sin ^2 (x) - cos ^2 (x)
-------------------------------
sin x cos x
We know that sin ^2 x - cos ^2 x = - cos (2x)
sin x cos x = 1/2 sin (2x)
Replacing
- cos (2x)
-------------
1/2 sin (2x)
Then it becomes
-2 cot (2x)