Buktikan bahwa ( sin x + cos x )² + ( sin x - cos x)²=2

Trigonometri

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

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

( sin x + cos x)² + ( sin x - cos x)² = 2
( sin x² + 2sinx cosx + cos x²) + ( sin x² - 2sinx cos x + cos x²) = 2
sin x² + 2sinx cosx + cos x² + sin x2 - 2sinx cosx + cos x² = 2

Ket : 2sinx cos x dicoret
(sin x² + cos x²) + (sin x² + cos x ²)= 2
1 + 1 = 2
2 = 2

Ruas kiri = Ruas kanan