(cosx + sinx) (cosx - sinx) = 1-2sin²x

(cosx + sinx) (cosx - sinx)
= cos x (cos x - sin x) + sin x (cos x - sin x)
= cos² x - cos x sin x + sin x cos x - sin² x
= cos² x - sin² x
= (1 - sin² x) - sin² x
= 1 - 2 sin² x

Ingat identitas trigonometri
[tex] \cos^{2} (x) + \sin^{2} (x) = 1 \\ \cos^{2} (x) = 1 - \sin^{2} (x) [/tex]

[tex] (\cos(x) + \sin(x) )( \cos(x) - \sin(x) ) \\ = { \cos^{2} (x) } - { \sin^{2} (x) } \\ = 1 - \sin^{2} (x) - \sin^{2} (x) \\ = 1 - 2 \sin^{2} (x) [/tex]
Semoga dapat dipahami