Question

BUKTIKAN

SIN^4X - COS^4X = 1 - 2 COS^2X

MAKSUDNYA NGG NGERTI. MOHON PENJELASANNYA

Answer 1

Verified answer

Bab Trigonometri
Matematika SMA Kelas X

sin⁴ x - cos⁴ x
= (sin² x + cos² x) (sin² x - cos² x)
= 1 . ( - (cos² x - sin² x))
= - (2 cos² x - 1)
= 1 - 2 cos² x

Answer 2

Verified answer

X^2 - y^2 = (x + y)(x - y)
sin^2 x + cos^2 x = 1
sin^2 x = 1 - cos^2 x

sin^4 x - cos^4 x
= (sin^2 x + cos^2 x) (sin^2 x - cos^2 x)
= (1) (sin^2 x - cos^2 x)
= (1 - cos^2 x) - cos^2 x
= 1 - 2 cos^2 x