# How do you prove tan x - 1 = (sin^2 x - cos^2 x)/(sin x cos x + cos^2 x)?

Numerator: $\left({\sin}^{2} x - {\cos}^{2} x\right) = \left(\sin x - \cos x\right) \left(\sin x + \cos x\right)$
Denominator: $\cos x \left(\sin x + \cos x\right)$
$\frac{N}{D} = \frac{\sin x - \cos x}{\cos} x = \tan x - 1$