How do you prove $cosx - sinx - cos^3x/cosx = sin^2x - tanx$ ?

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Answer 1 · 2015-07-03T02:59:08

Prove trig identity

$cos x - sin x - (cos^3 x)/cos x = (cos^2 x - cos^3 x - sin x)/cos x =$

$= (cos x(1 - cos^2 x) - sin x)/cos x = sin^2 x - sin x/cos x =$

$= sin^2 x - tan x$

How do you prove cosx - sinx - cos^3x/cosx = sin^2x - tanxcosx - sinx - cos^3x/cosx = sin^2x - tanx?