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

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Answer 1 · 2015-05-01T03:52:57

Numerator: $(sin^2 x - cos ^2 x) = (sin x - cos x)( sin x + cos x)$
Denominator: $cos x (sin x + cos x)$
$N/D = (sin x - cos x)/cos x = tan x - 1$

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