Nilai dari (sin x + cos x)²+(sin x - cos x)² =

(sinx+cosx)^2 + (sinx-cosx)^2
= (sin^2x+2sinxcosx+cos^2x) + (sin^2x-2sinxcosx+cos^2x
= sin^2x+cos^2x + sin^2x+cos^2x + 2sinxcosx-2sinxcosx
(ingat, sin^2x+cos^2x=1)
= 1+1
=2
inshaallah, semoga membantu:)

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

Ingat:
sin² α + cos² α = 1