SOLUTION: can you please prove this identity (tan x - cot x) / (tan^2 x - cot^2 x)= sin x cos x

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Question 434534: can you please prove this identity
(tan x - cot x) / (tan^2 x - cot^2 x)= sin x cos x
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
(tan x - cot x) / (tan^2 x - cot^2 x)= sin x cos x
..
start with left side
(tan x - cot x) / (tan^2 x - cot^2 x)
difference of squares
(tan x - cot x) / (tan x - cot x)(tan x + cot x)
1/(tan x + cot x)
1/((sinx/cosx)+(cosx/sinx))
1/((sin^2x+cos^2x)/sinxcosx))
1/(1/sinxcosx)=sinxcosx
verified:
Left side=Right side