Prove: sec^2 x - 2sec x cosx + cos^2 x = tan^2 x - sin^2 x

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sec^2 - 2secx cosx + cos^2x = tan^2x - sin^2x

(sec x - cos x)^2 = (sec ^2 x - 1) sin^2 x

Remember, sec^2x - 1 = tan^2 x :

(sec x - cos x)^2 = tan^2 x * sin^2 x

(sec x - cos x)^2 =( tan x * sin x )^2

(sec x - cos x) =sin x * sin x / cos x

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

Remember, 1 - cos^2 x = sin^2 x  :

sin^2 x = sin^2 x

x = x

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