Question

Nilai sin^4 x + cos^4 x = ...
A. (sin x + cos x)
B. (sin² x + cos² x)(sin² x - cos² x)
C. 1 - 1/2 sin² 2x
D. 1 - sin^-2 2x
E. 1 - 2sin² 2x

Mohon bantuannya beserta cara...
Sumber : Mandiri Matematika Kelas 2 SMA Program Ilmu Alam, Penerbit Erlangga

Answer 1

Verified answer

= sin⁴x + cos⁴x
= (sin²x)² + (cos²x)²
= (sin²x + cos²x)² - 2(sin x cos x)²
= 1 - sin²2x

E

Answer 2

Sin^4.x + cos^4 x
= (sin^2 x + cos^2 x)^2 -2sin^2 x. cos^2 x
= ( 1 )^2 - 1/2(4 sin^2 x cos^2 x)
= 1 - 1/2( 2sin x cos x )^2
= 1 - 1/2 sin^2 2x....(c)