Question

verify the identity
2(tan x-cot x)/tan^2 x-cot^2 x=sin 2x

Answer 1

2(tan x-cot x)/tan^2 x-cot^2 x
= 2(tan x-cot x)/(tan x-cot x)(tan x+cot x)
= 2/(tan x+cot x)
= 2/(sin x/ cos x + cos x/ sinx)
= 2/(sin ^2 x + cos ^2 x)/sin x cos x
= 2sin x cos x/(sin ^2 x + cos ^2 x)
= 2sin x cos x/(1)
= sin 2x

Answer 2

(tan x-cot x) cancels right?

Answer 3

yes

Answer 4

ohhh it cancels after you expanded the bottom

Answer 5

yes

Answer 6

im terrible at this concept, thanks so much

Answer 7

you are welcome