Question

Prove that `tanx-(sec^2x)/tanx=-cotx`?

Answer 1

`- cot x`

Explanation:

`E = tan x - (sec^2 x)/(tan x) = (tan^2 x - sec^2 x)/(tan x)`
Use trig identity:
`1 + tan^2 x = sec^2 x -> tan^2 x - sec^2 x = - 1`
We get:
`E = - 1/(tan x) = - cot x`