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**~berserk** This is the beginning of a couple of identities that i will probably need assistance on, all help given is greatly appreciated.

$\displaystyle \displaystyle{\frac{\tan x - \cot x}{\tan x + \cot x}=2\sin^2x-1}$

first i switched them all to sin and cos

then i found like denominators and combined

then i multiplied by the reciprocal leading me to here:

$\displaystyle \displaystyle{\frac{\sin x - \cos x}{\cos x \sin x} \bullet \frac{\cos x \sin x}{\sin x + \cos x}}$

then got $\displaystyle \displaystyle{\frac{\sin x - \cos x}{\sin x + \cos x} = 2\sin^2x-1}$

I'm unsure where to go from here