Sin⁴x + cos⁴x = a,maka nilai cos 4x adalah.. Mohon bantuannya

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

cos 4x = cos 2(2x)
= 2 cos^2 2x - 1
= 2 (cos 2x)^2 - 1
= 2 (cos^2 x - sin^2 x)^2 - 1
= 2 (cos^4 x - 2 cos^2 x sin^2 x + sin^4 x) - 1
= 2 (sin^4 x + cos^4 x - 2 sin^2 x cos^2 x) - 1
= 2 (a - (1 - a)) - 1
= 2 (a - 1 + a) - 1
= 2 (2a - 1) - 1
= 4a - 2 - 1
= 4a - 3

^ = pangkat