Trigonometri rasa aljabar. Operasikan bentuk berikut
[tex]\displaystyle 2\left ( \sin^6 x+\cos^6 x \right )-3\left ( \sin^4 x+\cos^4 x \right )[/tex]
[tex]\displaystyle 2\left ( \sin^6 x+\cos^6 x \right )-3\left ( \sin^4 x+\cos^4 x \right )[/tex]
Verified answer
PEMBAHASAN
Trigonometri
sin² x + cos² x = 1
(sin² x + cos² x)³
= sin⁶ x + cos⁶ x + 3 sin² x cos² x (sin² x + cos² x)
= sin⁶ x + cos⁶ x + 3 sin² x cos² x
(sin² x + cos² x)²
= sin⁴ x + cos⁴ x + 2 sin² x cos² x
2(sin⁶ x + cos⁶ x) - 3(sin⁴ x + cos⁴ x)
= 2 ((sin² x + cos² x)³ - 3 sin² x cos² x) - 3 ((sin² x + cos² x)² - 2 sin² x cos² x)
= 2 (1 - 3 sin² x cos² x) - 3 (1 - 2 sin² x cos² x)
= 2 - 6 sin² x cos² x - 3 + 6 sin² x cos² x
= 2 - 3
= -1