Bentuk sederhana dari 1+sin 4x+cos 4x/1+sin 4x-cos 4x

Jawaban:

(sin 4x – sin x)² + (cos 4x – cos x)²

= (sin² 4x + sin² x – 2sin 4x sin x) + (cos² 4x + cos² x – 2cos 4x cos x)

= (sin² 4x + cos² 4x) + (sin² x + cos² x) – 2(cos 4x cos x + sin 4x sin x)

= 1 + 1 – 2 cos (4x – x)

= 2(1 – cos 3x)