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

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